Method to assess the physical effort to acquire physical targets

ABSTRACT

An objective, quantitative metric is used in a system that measures the physical effort expended by a user on computer input devices while the user manages the functionality of application software so that an evaluation of the desirability of computer-human interfaces being evaluated is generated. For certain convex polygonal targets of arbitrary size and location relative to a target acquiring device, the present invention identifies a circular subset of points that permits determination of the width and distance parameters of Fitts&#39; Index of Difficulty and thus, permits objective quantification of the physical effort incurred in acquiring a target via computer input devices. The invention itself presents a method for symbolically expressing actual targets appearing on a computer-human interface and physical actions required by a user to accomplish a task set utilizing the application software. This symbolic capability also presents procedures for storing relevant alterations to actual targets occasioned by user manipulations. Targets to which the invention applies are computer interface entities in the shapes of triangles, standard rectangles, parallelograms, trapezoids, and general convex quadrilaterals.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates generally to computer software metrics and, morespecifically, to defining and utilizing a metric that provides anobjective, quantitative method of evaluating the physical effortrequired to manipulate a computer-human-interface.

2. Description of the Prior Art

The prior art employs various techniques to design a computer-humaninterface. Among these are subjective techniques which utilizeexperience and intuition to appraise existing or proposed interfacedesigns and generally result in lists of specific recommendations thathave historically been found integral to good interface design (Mayhew,Deborah, Principles and Guidelines in Software User Interface Design,1992), (Smith, S. L. and Mosier, J. M., Design Guidelines for UserInterface Software, 1986). However, it is not always apparent thatresulting recommendations are applicable to new technologies since,being based on phenomenologic observation, the scope of theirapplicability is uncertain.

Less subjective approaches to interface design comprise such proceduresas prototyping, focus groups, cognitive walk-throughs, and alpha tests.A review of writings of those skilled in these arts (Dix, A., Finley,J., Aboud, G., Beale, R., Human-Computer Interaction, 1993),(Shneiderman, B., Designing the User Interface: Strategies for EffectiveHuman-Computer Interaction, 1992); (Dumas, J., Designing User Interfacesfor Software, 1988) convey that similarities exist between differentpractitioners. In general, these experts advocate: (1) employ practicalexperience, (2) use applicable experimental findings, (3) userules-of-thumb, (4) promote consistency. Attempts to apply practicalexperience and rules-of-thumb confront the analyst with the samequandaries of observed with the subjective approaches. Althoughexperimental results can be of significant worth, implications of theartificial setting under which experiments are typically conducted mustbe appraised for applicability to the production environmentanticipated. Finally, the provision of consistency, while widelyadvocated, has proved difficult to achieve since an objective,quantitative definition of consistency has yet to be formulated. (PayneS. J. and Green, T. R. G., Task-Action Grammars: A model of the mentalrepresentation of task languages, Computer-Human Interaction, 1986, pp.93-133)

Dumas and Redish (Dumas, J. S. and Redish, J. C. A Practical Guide toUsability Testing, 1993), (Hix, Deborah and Hartson, H. Rex, DevelopingUser Interfaces: Insuring Usability Through Product and Process, 1993)summarizes the prior art for comparing existing interfaces: (1) provideexpert review of the design, (2) perform peer walk-through, (3)prototype, and (4) monitor behavior of the production environment viaone-way mirrors, logs, video tapes, and questionnaire interviews. Ofthese, expert review has been shown inadequate when performed by asingle expert but of benefit when performed by a group of outsideexperts (Jeffries, R., Miller, J. R., Wharton, C., and Uyed, C. M., UserInterface Evaluation in the Real World, Proceedings of CHI '91, HumanFactors in Computing Systems, 1991, pp. 119-124.). While frequentlyemployed to advantage, peer walk-through and prototyping have thedisadvantage of producing difficult to reproduce, subjectiveevaluations. The monitoring of production environments capturesextensive data, but such data only offer the opportunity of objectivequantification; there remains the need to define the methodology forconverting such data into recognized, quantitative measures thataccurately reflect usability.

Since it predicts the time required to acquire a target, some expertsproffer Fitts' Law as the basis for an objective, quantitative metric ofthe effort expended during physical actions that acquire a stationarytarget. An expression of Fitts' Law is: ##EQU1## where: TT Total timefor target acquisition (seconds).

RT Reaction time (seconds).

b Muscle transfer rate (seconds per bit).

I Index of Difficulty (bits).

W_(t) Width of target (linear units).

D_(t) Distance to target (linear units).

This invention relates to the implications of how users perceive theD_(t) and W_(t) parameters of the Index of Difficulty: ##EQU2## Fitts(Fitts, P. M., The information capacity of the human motor system incontrolling amplitude, Journal of Applied Psychology, 1954, pp. 381-391)implicitly set k=0 by excluding k from his original formulation. Welford(Welford, A., The Fundamentals of Skill, 1968) proposed k=0.5, arguingthat this offers a superior fit to published empirical data. MacKenzie(MacKenzie, I., Fitts' Law as a research and design tool inhuman-computer interaction, Human-Computer Interaction, 1992, pp.91-139) reappraised the use of Shannon's Information theory (Shannon andWeaver, The Mathematical Theory of Communication, 1949) as the basis ofFitts' Law and concluded that k=1 offers an even better fit to publishedempirical data. Analysis presented below in the section "Analysis ofArbitrary Triangular Targets" shows that k is not relevant to the user'sdetermination of either target distance or target width.

Studies (Welford, op. cit.), (Jagacinski, R. J. and Monk, D. L., Fitts'Law in two dimensions with hand and head movements, Journal of MotorBehavior, 1985, pp. 77-95); (Jagcinski, R. J., Repperger, D. W., Moran,M. S., Ward, S. L., and Glass, B., Fitts' Law and the microstructure ofrapid discrete movements, Journal of Experimental Psychology, 1980, pp.309-320.) show that times for hand-homing in either direction betweenkeyboard and mouse conform to Fitts' Law. It has also been shown thatfinger targeting between keys follows Fitts' Law when 7W_(t) ≦D_(t).Experimental evidence (Card, S. K., English, W. K., and Burr, B. J.,Evaluation of the mouse, rate-controlled isometric joy stick, step keys,and text keys for text selection on a CRT, Ergonomics, 1978, pp.601-613); (Jagacinski and Monk, op. cit.); (MacKenzie, op. cit.) alsoindicates that Fitts' Law can be applied to CRT environments that employthe mouse controlled cursor. Verification of the applicability of Fitts'Law to mouse movement in real world systems in general requiresadditional study since cursor control experiments typically employcircular or square targets rather than the more diverse target shapesfound in production environments.

The present invention contends that failure of practitioners of theprior art to successfully offer a defensible definition for the D_(t),and W_(t) parameters of Fitts' Index of Difficulty that is applicable toarbitrary targets has rendered its general application unfeasible.Investigating implications of this failure starts by recalling that theaspect ratio (AR) of a target is defined as ##EQU3## Since personsutilizing Fitts' Law generally define W_(t) of circular and squaretargets to be the diameter and the length of a side respectively,studies which employ the prior art generally apply to physical targetsfor which unitary aspect ratios pertain. For such targets the prior artgenerally defines, D_(t), to be the distance from the cursor to thetarget center although some practitioners of the prior art question theapplicability of these definitions of D_(t) and W_(t) for targets of0<AR<<1 and 1<<AR<∞. (Gillan, D., Holden, K., Adam, S., Rudisill, M.,Magee, L., How Does Fitts' Law Fit Pointing and Dragging, Proceedings ofCHI '90; Human Factors in Computing Systems, 1990, pp. 175-182). FIG. 1conveys implications of these definitions. Parts A through C of FIG. 1depict rectangular targets of AR=1, AR>1, and AR<1 respectively, whilePart D depicts a convex polygon of triangular shape. For these targetsthe prior art generally defines locations 1A08, 1B08, and 1C08 as theterminus of user traverses into respective physical targets. Underdefinitions prevailing in the prior art target distances, D_(t), aredepicted by ##EQU4## for the said targets respectively. For the squaretarget, 1A02, the width and distance definitions are specific, butcharacteristics of the remaining targets do not permit this specificityfor either width or distance definitions. Location 1D08 is not soappraised as triangular targets are not generally covered by studiesinvestigating Fitts' Law.

Defining a constrained target to be a target for which the userconsiders all target sides when choosing a traverse to the target,research involved with the present invention concludes on logicalgrounds that traditional definitions of target width and distance arevalid only for constrained squares and circles. Data collected andanalyzed during development of the present invention provideexperimental results showing there are statistically significantdifferences between mean target acquisition points and centers oftargets of the types depicted by FIG. 1 Parts B through D. Theseempirical results indicate that users confronting interface environmentsdepicted by FIG. 1 Parts B through D with initial cursor locations at1B18, 1C18, 1D18 will take traverses 1B16, 1C16, and 1D16 and generallyhave modal termination points at 1B06, 1C06, and 1D06 respectivelyrather than traverses 1B14, 1C14, and 1D14 with termination points at1A08, 1B08, and 1C08 as suggested by the prior art. It is shown belowthat spatial equivalence between 1A06 and 1A08 arises from the geometryof a small, square target and not from predictive ability of the priorart.

In seeking definitions which better reflect user behavior during targetacquisition, MacKenzie (op. cit.) offers the following: (1) theperimeter definition: W_(t) =H+L, (2) the area definition: W_(t) =H×L,and (3) the angle-of-approach definition: ##EQU5## The perimeterdefinition implies that a square target of H=L=3 and an elongatedrectangular target of H=0.5 and L=5.5 have equal W_(t). Under the areadefinition, a square of H=L=3 and an elongated rectangular target ofH=0.5 and L=18.0 also have equal W_(t). MacKenzie does not offertheoretical justification or empirical evidence of why such diverseshapes have equivalent Wt values nor does he indicate how to determineD_(t).

The angle-of-approach definition specifies target width to be the lengthof the segment subtended by parallel sides of the target when thetraverse is extended through the target, the midpoint of this segmentbeing the traverse terminus. Employing Information Theory, researchinvolved with the present invention shows that rational users facing arectangular target constrained in the narrow dimension will seek anacquisition point on the axis-of-symmetry; namely, line 216 of FIG. 2.The research conducted for this invention empirically corroborates thisconclusion for constrained targets. Lines 204 and 220 of FIG. 2,represent limits to user targeting since traverses terminating to theleft of 204 or to the right of 220 are to locations which entaildecreasing W_(t) and either a decreasing D_(t) or a D_(t) increasingless rapidly than Wt decreases. For either case traverses into theseareas result in an increase of the index of difficulty. It follows thatunder the angle-of-approach definition, the rational user will terminatea traverse to a rectangular target on line 216 between locations 218 and240.

Given these conclusions, it is possible to compare the effort oftraversing two arbitrary paths from initial cursor location 212 to theline segment defined by points 218 and 240 of FIG. 2. Thus, compare pathCUMV having ##EQU6## with path CRNS having ##EQU7## The effort ofacquiring the target using point 236 as the acquisition point is:##EQU8## It is thus logically concluded that under the angle-of-approachhypothesis traverses terminating on the line connecting points 230 and240 will be perceived by users as requiring equal physical effort.

To determine whether users show indifference to the traverse taken toacquire a rectangular target of non-unitary aspect ratio, the researchperformed for the present invention included an experiment in whichsubjects completed repeated trials to such a target within a fixedenvironment. Analysis of data from this experiment investigated thefootprint of hits generated to ascertain whether hits were randomlydistributed along the line connecting points 218 and 240 as would beexpected if all traverses entail equal physical effort. Hits were foundto be non-randomly distributed along said line segment, instead having amodal location related to the initial position of the cursor. Therefore,research involved with the present invention concludes theangle-of-approach for target width can be rejected on both logical andempirical grounds.

Those experienced in the art of design and evaluation of computer-humaninterfaces thus recognize that the prior art is inadequate to: (1)express objectively each operation users perform on computer inputdevices during a terminal session, (2) identify the Distance and Widthparameters of Fitt's Index of Difficulty for other than square orcircular targets, and (3) specify in an objective, quantitative mannerthe physical effort of performing a specified set of computer tasks.

Accordingly it is an objective of the present invention to provide anInterFace Grammar capable of recording all physical operations usersperform on a computer-human interface during a terminal session in amanner to permit subsequent quantitative analysis. It is anotherobjective to provide a defensible method for determination of thedistance and size of the implicit target contained within triangular andconvex quadrilateral targets of arbitrary size, location, andorientation relative to a target acquiring entity. Finally, it isanother objective to provide a method for aggregating the effortexpended in acquiring individual targets into an index suitable foridentification of that interface which requires lowest total physicaleffort for performance of a given task set.

SUMMARY OF THE INVENTION

Utilization of the present invention can benefit persons involved withapplication software in three ways. First, the invention aids design ofthe computer-human interface (CHI) of new software systems. Duringdesign of application software various CHI are proposed to manage itsfunctionality and a decision made regarding the CHI to actually develop.Employment of the invention permits designers to infer the level ofphysical effort required to manipulate a proposed CHI prior to creationof the interface and thus objectively appraise a major component of aninterface's user friendliness. Design is additionally benefited by theinvention as it permits the designer to appraise syntactic consistencyprior to interface coding. Since syntactic consistency greatlyinfluences the "learnability" of a proposed interface this benefitpermits enhancing a major component requisite to the commercial successof a new application software. Second, the invention enables prospectivebuyers to appraise currently marketed software application systems thatprovide the functionally sought. By applying the invention to eachsoftware system being evaluated via a standard test suite that reflectstypical demands required of the application system, an objective,quantitative appraisal of the expected physical effort expended duringnormal use of each software system will identify the system requiringleast expenditure of physical effort. Additionally, appraisal ofinformation prepared during application of the invention permits insightinto the "learnability" of the contending systems. Third, individualusers may be evaluated in a non-invasive manner to appraise the physicaleffort each expends to accomplish an assigned task set. This permitsobjective identification of which workers employ the softwareefficiently and those which are less efficient. From these results itbecomes possible to objectively defend a reward system for the formerand retraining or transfer programs for the latter.

Thus, in one aspect, the present invention is a computer-implementedmethod for selecting from a plurality of extant or proposed differentcomputer-human interfaces an optimum computer-human interface thatprovides a low level of aggregated physical effort for the human toacquire and manipulate a displayed physical target. First, the operativeacquiring entity is identified. The present invention proceeds byidentifying the start location of the acquiring entity. Then the presentinvention iterates over the steps of each task of the pre-definedstandard test suite utilizing each of the computer-human interfaces.First, a first circle of maximum radius is inscribed within the physicaltarget of one of the computer-human interface. Then the radius of theinscribed first circle is determined. The distances from each apex ofthe physical target to the center of the inscribed first circle isdetermined. For each apex a maximum equi-target locus circular arccentered at the midpoint of the line connecting the respective apex andthe center of first circle with radius of one-half each respectivedistances is generated. If the acquiring entity is located on the borderor outside of each of the maximum equi-target locus circular arc, themodal place of acquisition is determined to be the center of theinscribed first circle. If the respective maximum equi-target locuscircular arc contains the acquiring entity, then the modal place ofacquisition is determined to be the center of a second circle inscribedwithin the physical target, with the center of the inscribed secondcircle being a function of the horizontal displacement and verticaldisplacement of the acquiring entity from the apex. The level ofphysical effort of one of the computer-human interfaces needed toacquire the physical target is determined as a relation of the distancebetween the start location of the acquiring entity to the selected modalplace of acquisition and the radius of the circle identified by theselected modal place. The level of physical effort so determined of oneof the computer-human interface is aggregated and stored. The storedlevel of aggregated physical effort is compared with anothercomputer-human interface. The optimum computer-human interface isselected that provides a low level of aggregated physical effort asdetermined by the comparison step.

In another aspect, the present invention is a computer-based method ofrepresenting computer-human interactions to enable a comparison of aplurality of physical operations performed in the computer-humaninteractions. First, a physical operator rule grammar is defined toinclude classes of physical operations and their instantiations ofphysical operations. The physical operator rule grammar is defined toinclude interrelationships of the classes to represent thecomputer-human interactions. A first computer-human interaction isstored into the memory of the computer system.

A stored first computer-human interaction is compared with the physicaloperator rule grammar to identify the instantiation that corresponds tothe first computer-human interaction. The first instantiation thatcorresponds to the first computer-human interaction is stored in memoryas a representation of the first computer-human interaction.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1D contain four CRT targets having arbitrary height and widthdimensions and an arbitrarily positioned acquiring entity. Pathsdepicted by dotted lines reflect observed typical traverses users taketo each target given the initial locations depicted for the acquiringentity

FIG. 2 is a rectangular target of non-unitary aspect ratio and aninitial acquiring entity position employed to critique theangle-of-approach definition of target width and distance.

FIG. 3 is a triangular target of arbitrary height and arbitrary initialacquiring entity position employed to illustrate development of theimplicit target method.

FIG. 4 is a scalar triangular target with illustrative initial acquiringentity locations and exemplar Equi-Target Loci to illustrate applicationof implicit target analysis to triangular targets.

FIGS. 5A-5F contain six quadrilateral targets illustrating that theintersection of two triangles of appropriate shape and orientationsuffice to generate a convex, arbitrarily shaped quadrilateral target.

FIG. 6 is an arbitrary convex quadrilateral target generated by twoexemplar triangles that illustrates identification of the primarygenerating triangle.

FIG. 7 is an arbitrary convex quadrilateral target, an acquiring entitylocation, and exemplar Equi-Target Loci to illustrate application ofimplicit target analysis to quadrilateral targets.

FIG. 8 is a rectangular target, an acquiring entity location, andexemplar Equi-Target Loci to illustrate application of implicit targetanalysis to rectangular targets.

FIGS. 9A-9T contain a plurality of varied sheets employed by the exampleto illustrate application of the present invention:

FIG. 9A is a CRT depiction of the GUI environment of the example thatalso shows graphic objects and text specified by the standard testsuite.

FIG. 9B through FIG. 9E is InterFace Grammar code specifying artifactsof the Graphic User Interface appearing on FIG. 9A.

FIG. 9F through FIG. 9G are exemplar task templates appropriate todefining method templates capable of performing sub-goals of theexample.

FIG. 9H through FIG. 9K are exemplar method templates appropriate toperforming sub-goals of the example.

FIG. 9L displays in expanded form the method and tasks employed toaccomplish Sub-Goal #3 of the example using spider menu based selection.

FIG. 9M displays methods employed, InterFace Grammar code generated, andphysical effort expended to accomplish the test suite when utilizingdrop-down menu bar initiated function activation.

FIG. 9N is a CRT depiction of traverses executed to accomplish the testsuite when utilizing drop-down menu bar initiated function activation.

FIG. 9O displays methods employed, InterFace Grammar code generated, andphysical effort expended to accomplish the test suite when utilizingicon initiated function activation.

FIG. 9P is a CRT depiction of traverses executed to accomplish the testsuite when utilizing icon initiated function activation.

FIG. 9Q displays methods employed, InterFace Grammar code generated, andphysical effort expended to accomplish the test suite when utilizingspider menu initiated function activation.

FIG. 9R is a CRT depiction showing traverses executed to accomplish thetest suite when utilizing spider menu initiated function activation.

FIG. 9S displays methods employed, InterFace Grammar code generated, andphysical effort expended to accomplish the test suite when utilizingkey-equivalent initiated function activation.

FIG. 9T is a CRT depiction showing traverses executed to accomplish thetest suite when utilizing key-equivalent initiated function activation.

FIGS. 10A-10B contain two high level flowcharts showing a programmingenvironment appropriate to implementing the invention:

FIG. 10A is a flowchart of an environment appropriate to design ofcomputer-human interfaces for new application systems.

FIG. 10B is a flowchart of an environment appropriate to evaluation ofexisting computer-human interfaces.

FIGS. 11A-11G contain seven high level flowcharts detailing thepreferred implementation of implicit target identification:

FIG. 11A details the root calling procedure.

FIG. 11B is the Detailed Analysis of the Triangle.

FIG. 11C and FIG. 11D is the Detailed Analysis of the Quadrilateral.

FIG. 11E is the Detailed Analysis of the Trapezoid.

FIG. 11F is the Detailed Analysis of the Standard Rectangle.

FIG. 11E is the Detailed Analysis of the Parallelogram.

FIGS. 12A-12D contain four triangular targets illustrating the preferredapproach to implicit target identification for this class of target:

FIG. 12A illustrates identification of the largest circle which can beinscribed within a triangle.

FIG. 12B illustrates an acquiring entity location outside the influenceof all MaxETL.

FIG. 12C illustrates an acquiring entity location within the region of aMaxETL, the ETL pertaining to that said location and parameters of theaxis transformation performed.

FIG. 12D illustrates the axis after transformation and theidentification of the implicit target appropriate to the CRTenvironment.

FIG. 13A-13E contain five quadrilateral targets illustrating thepreferred approach to implicit target identification for this class oftarget:

FIG. 13A illustrates determination of the coordinates of the two finiteexternal apexes, identification of the largest and smallest inscribedextreme circles of each generating triangle, and identification of theprimary triangle.

FIG. 13B illustrates identification of the MaxETL for each target apex,the MaxETL for external apex, and identification of the implicit targetto be the largest inscribed circle when the acquiring entity is on oroutside the bounds of all MaxETL.

FIG. 13C illustrates an acquiring entity location within the region ofan apex MaxETL and the ETL pertaining to that acquiring entity location.

FIG. 13D illustrates an acquiring entity location within the region ofthe external apex MaxETL such that the center of the implicit targetfalls on the line connecting the centers of the smallest and largestinscribed extreme circles.

FIG. 13E illustrates adjustment to the implicit target location when theacquiring entity is within the region of the external apex MaxETL suchthat the optimal implicit target falls outside the actual target.

FIGS. 14A-14E contain five trapezoidal targets illustrating thepreferred approach to implicit target identification for this class oftarget:

FIG. 14A illustrates determination of the coordinates of the singlefinite external apex, location of the inscribed extreme circles of eachgenerating triangle, and identification of the primary triangle.

FIG. 14B is a trapezoidal target having a primary triangle with infiniteexternal apex that illustrates axis transformation and identification ofthe MaxETL for target apexes and the external apex.

FIG. 14C is a trapezoidal target having a primary triangle with infiniteexternal apex that illustrates an acquiring entity within the region ofa target apex MaxETL and the ETL pertaining to said location.

FIG. 14D is a trapezoidal target having a primary triangle withinfinitely remote external apex that illustrates identification of theimplicit target for the case of an acquiring entity outside theinfluence of all apex MaxETL when a normal approach to the lineconnecting the centers of the inscribed extreme circles is not possible.

FIG. 14E is a trapezoidal target having a primary triangle withinfinitely remote external apex that illustrates identification of theimplicit target for the case of an acquiring entity outside theinfluence of all apex MaxETL when a normal approach to the lineconnecting the centers of the inscribed extreme circles is possible.

FIGS. 15A-15H contain a plurality of standard rectangular targetsillustrating the preferred approach to implicit target identificationfor this class of target:

FIG. 15A illustrates identification of the primary triangle and locationof the inscribed extreme circles of the primary triangle.

FIG. 15B illustrates axis translation and identification of the apexMaxETL for the transformed axis.

FIG. 15C illustrates the case of an acquiring entity located within theMaxETL of an apex, the ETL pertaining to said location, and parametersof the reflection to be performed.

FIG. 15D illustrates the result of acquiring entity reflection andidentification of the implicit target for the reflected system.

FIG. 15E illustrates the case of an acquiring entity located outside theinfluence of all apex MaxETL from which a normal approach to the lineconnecting the centers of the two inscribed extreme circles can beperformed.

FIG. 15F illustrates the result of acquiring entity reflection andidentification of the implicit target for the transformed system.

FIG. 15G illustrates the case of an acquiring entity located outside theinfluence of all apex MaxETL from which a normal approach to the lineconnecting the centers of the two inscribed extreme circles cannot beperformed.

FIG. 15H illustrates the result of acquiring entity reflection andidentification of the implicit target for the transformed system.

FIGS. 16A-16H is a plurality of parallelogram targets illustrating thepreferred approach to implicit target identification for this class oftarget:

FIG. 16A illustrates identification of the primary triangle and locationof inscribed extreme circles of the primary triangle.

FIG. 16B illustrates axis translation and identification of the apexMaxETL for the transformed axis.

FIG. 16C is the case of an acquiring entity located within the MaxETL ofthe apex in the upper-right quadrant and the ETL pertaining to thatacquiring entity location.

FIG. 16D illustrates identification of the implicit target for the givenscenario.

FIG. 16E is the case of an acquiring entity outside the influence of allapex MaxETL and located such that a normal approach to the lineconnecting the centers of the two inscribed extreme circles is possible.

FIG. 16F illustrates the result of acquiring entity reflection, physicaltarget reflection, and implicit target identification for thetransformed system.

FIG. 16G is the case of an acquiring entity in the upper left quadrant,outside the influence of all apex MaxETL and located such that a normalapproach to the line connecting the centers of the two inscribed extremecircles cannot be performed.

FIG. 16H illustrates the result of acquiring entity reflection, physicaltarget reflection, and implicit target identification for thetransformed system.

FIGS. 17A-17B is two spider menus illustrating application of implicittarget analysis to a non-typical menu design.

FIG. 17A illustrates a seven option display.

FIG. 17B illustrates display when sub-options are displayed.

DETAILED DESCRIPTION OF THE INVENTION

Formalisms well understood by those familiar with the mathematical artsare employed to justify the procedures herein contained. Theseformalisms are presented to validate procedures of the preferredembodiment which, given the initial location of the target acquiringentity, identify the unique subset of points within a physical targetdisplayed by a computer-human interface that forms the basis of anobjective, quantitative measure of the physical effort expended duringtarget acquisition.

For the purpose of this invention a procedure is perceived by thosefamiliar with the computing arts as a self-consistent sequence of stepsisomorphic to the steps implicit in the mathematical formalisms thatunderpin the goal of identifying the set of points within physicaltargets which best reflect user hit footprints during acquisition of atarget displayed by a human-computer interface. Accomplishing individualsteps of the procedures presumes manipulation of magnetic signals withinthe computer which are capable of storage, location transfer, andlogical manipulation. To communicate these processes it is usually,though not necessarily required that the unique internal arrangements ofsignals which reflect the isomorphism of the interface targetmanipulations be expressed in terms which reflect human perceptions oftarget analysis. It is appreciated that whereas this terminology permitsthose experienced in the interface art to communicate betweenthemselves, as implemented by the invention these terms are only labelsconvenient to humans to represent unique physical quantifies actuallyexisting within the magnetic mediums of the computer.

Further, terms implied and employed by the procedures relate tomathematical manipulations commonly performed by humans of requisiteskill. Realization of such capability by a human is not implied, norgenerally desirable, during the actualization of the invention which isexpected to be performed by computer operations directed by proceduresimplicit to the preferred implementation presented below. The saidprocedures are applied to a symbolic representation of expected oractual human activity on computational machinery which will generally,but not necessarily, be a general purpose computer. To those experiencedin the programming arts, the manner of accomplishing any particularmanipulation will not ordinarily be unique. Thus, it is contemplatedthat many changes and modifications may be made to the detaileddescription of the invention by one of ordinary skill in the art withoutdeparting from the spirit and scope of the invention.

In the following description, numerous details are presented that employgeometric, matrix algebra, and other formalisms of the mathematical andcomputational arts which can be more readily comprehended throughemployment of definitions and nomenclature pertinent to the presentinvention. It is to be recognized that certain mathematical formulationsand computational procedures not explicitly detailed are present byimplication to those skilled in the requisite arts. Additionally, it isapparent to those skilled in these arts that the present invention maybe described utilizing different notation without these specificdetails.

It is to be appreciated that in mathematical development reference toattributes of an object rather than to the object itself is commonlyrequired. Rather than applying unique integer identifiers to referenceindividual attributes of a entity depicted by a figure, a single integeris assigned to identify said entity and as required to differentiateseparate attributes of the entity itself, additional symbols readilyunderstood by those knowledgeable in the mathematical arts will beaffixed to the entity identifier. An instance of this approach is toreference a line by an integer, XXX, and reference the length of saidline by ##EQU9## An additional relevant instance pertains to a pointdisplayed on the CRT screen. Said point may be identified by AAA, theCartesian location of said point identified by (AAA_(X), AAA_(Y)), anddirectional X and Y displacement by AAA_(X) and AAA_(Y) respectively.Other instances of entity attribution rather than entity identificationper se utilizes mathematical notation in conjunction with the entityidentifier in manners well understood by those of normal skill in themathematical arts.

FORMAL FOUNDATION OF THE INVENTION

Fitts opined that users envisage a specific point within the target tobe the lowest effort acquisition point, but muscle tremor, inattention,fatigue, etc. result in physical target acquisition occurring at otherthan this optimal point. Applying Fitts' observation, this inventionposits that the footprint of hits obtained from repeated trials in aconstant environment represents the user's balance between theadditional physical effort expended when performing a sub-optimumtraverse and the value of time and effort required to achieve a moreoptimum traverse. This footprint of hits is termed the "ImplicitTarget." The foundation of the invention additionally posits that usersenvisage the center of the implicit target to be the center of thelargest circular footprint inscribed within the target commensurate withminimizing the Index of Difficulty. This contention of individualbehavior is justified by the whole of economic science which ispredicated on the presumption that individuals conduct themselves toeither maximize gain from a given effort or attain a given goal at leasteffort. This concept has been explicitly applied to how individualsoptimize physiologic resources. (Navon and Gopher, On the Economy of theHuman-Processing System, Psychological Review, 1979, pp. 214-255).Finally, the foundation of the invention posits that if the implicittarget can be identified, its distance, D_(t), and width, W_(t), can beutilized by the Index of Difficulty to provide a valid measure of theeffort expended to acquire said target. Research involved in the presentinvention concludes that for typical human-computer interfaceenvironments, the assumption that users seek to minimize the physicaleffort incurred while acquiring the physical target does permitpredicting the diameter and location of the implicit target. Datacollected for the present invention show that within limits identifiedby prior studies, user behavior during acquisition of targets withnon-unitary aspect ratios can be described by Fitts' Law to an accuracysufficient to aid interface design.

Analysis of Arbitrary Triangular Targets

Determining the extent of angle δ of arbitrary apex "a" of arbitrarytriangle Δabc proceeds by determining the length of the triangle's sidesvia the equation: ##EQU10## with application of the Law of Cosines todetermine δ. ##EQU11##

FIG. 3 illustrates the environment of a triangular target of arbitrarilylarge height in the direction of the X-axis. The physical target has anapex at the axis origin 304 formed by the intersection of sides 307 and309 and has 316 as the bisector of said apex, said bisector beingcoincident with the X-axis. Bisector 316 and target side 307 form angle308. The acquiring entity, 305, at location (302_(X), 303_(Y)), isarbitrarily positioned relative to the 304 origin. The distance, 306, tothe physical target is the length of the traverse to the unknown butoptimal acquisition point 311 located at coordinates (X_(t),0). Circle313 denotes the largest circle centered at 311 on line 316 that can beinscribed between the sides forming apex 304. The radius, R_(t), of thiscircle and its distance, D_(t), are determined by:

    R.sub.t =X.sub.t sin θ                               (Eq. 4) ##EQU12## where: X.sub.t =310.sub.X

θ=308

X_(c) =302_(X)

Y_(c) =303_(Y)

To determine the coordinates of the target acquisition point whichminimizes the Index of Difficulty, express the Index of Difficulty,I_(t), as: ##EQU13## I_(t) is a strictly increasing function since##EQU14## for all t. Because the value of X_(t) which minimizes astrictly increasing function of a function, F(G(X_(t))), is the value ofX_(t) which minimizes G(X_(t)), the value of X_(t) which minimizes I_(t)is the same value which minimizes ##EQU15## Therefore: ##EQU16##

Since X_(t) sin θ≠0 for any X_(t) >0 and all possible θ of convexpolygonal targets, the preceding can be multiplied by (2X_(t) sin θ)²and terms rearranged to obtain: ##EQU17## Canceling terms gives:##EQU18## Because X_(t) -X_(c) ≠0 for X_(t) ≠0 it follows that ##EQU19##which gives: ##EQU20##

Given the initial acquiring entity location, the coordinates of thecenter of the implicit circular target of r=X_(t) sin θ which permitlowest physical effort target acquisition are: ##EQU21##

To consider which acquiring entity locations have a given inscribedcircle as the implicit target of lowest physical effort, complete thesquare for X_(t) X_(c) =Y_(c) ² +X_(c) ² : ##EQU22## Rewriting gives:##EQU23## This represents a circle having its center at coordinates##EQU24## with radius of ##EQU25##

FIG. 4 aids interpretation of these results. For an arbitrary circularfootprint 448 within an arbitrary, scalene, triangular physical target480 having center 444 on the bisector, 404, of 400 and having tangentswith at least two sides of the triangle, there exists a locus of points,420, comprising a circular arc for which this inscribed circle will bethe implicit target of least acquisition effort. This arc is termed the"Equi-Target Locus", (ETL). From preceding results, the radius,##EQU26## of the ETL for the implicit target centered at 444 is:##EQU27## with center at: ##EQU28##

There exists a unique ETL_(n) for each 0<X_(n) ≦X_(m). Circular arcs 420and 442 exemplify ETL for two of the infinite number of possibleimplicit targets centered on line 404.

To appraise user behavior from different locations on a single ETLconsider two arbitrary initial acquiring entity locations 422 and 426 onETL 420. Since these locations are on the same ETL, the user willapproach the same implicit target from either 422 or 426 to arrive nearthe optimal acquisition point 444 even though unequal levels of physicaleffort are expended to acquire the physical target. The validity of thisstatement is apparent by noting that traverses from 422 and 426 entailtraverses of ##EQU29## respectively. Target width ##EQU30## i.e.,2×R_(n), is common to both traverses. Since ##EQU31## it follows that:##EQU32##

Because the above logic applies to each apex of physical target 480there exists a "Maximum Equi-Target Locus" (MaxETL): i.e., 442_(MaxETL),470_(MaxETL), and 464_(MaxETL) for apexes 400, 482, and 458respectively. When combined 442_(MaxETL), 470_(MaxETL), and 464_(MaxETL)form the inner boundary of the 456 region. For initial acquiring entitylocations within the 456 region the effort to acquire the triangulartarget is minimized when 450, the center of the largest inscribed circle454, is selected as the optimal acquisition point. Thus, acquiringentity locations 430 and 434 both have 450 as the center of a commonimplicit target; 454, even though the physical effort from location 430is greater than from location 434.

Analysis of Arbitrary Convex Quadrangular Targets

FIG. 5 conveys that any convex, quadrilateral target can be defined bythe intersection of two appropriately shaped and positioned triangleswhich the present invention terms "Generating Triangles." The apex of agenerating triangle which is not an apex of the physical target will betermed an "External Apex". When an external apex is generated by twoconverging sides of a generating triangle it will be termed a "FiniteExternal Apex". An "Infinite External Apex" is to be considered atheoretical intersection at infinite distance of the parallel sides of agenerating triangle of infinite height.

FIG. 5A depicts that two generating scalene triangles of finite height(generating triangles being indicated by light dashed lines) produce thegeneral convex quadrilateral (physical targets being indicated by heavysolid lines). FIG. 5B depicts that when one generating triangle is offinite height and one is of infinite height the trapezoid subclass ofquadrilateral is produced. When the triangle of finite height isisosceles the regular trapezoid results. FIG. 5C and FIG. 5D depict thattwo generating triangles of infinite height with non-orthogonal sidesproduce the parallelogram. FIG. 5C depicts that generating triangles ofunequal bases, produce the general parallelogram, while FIG. 5D depictsthat generating triangles of equal base lengths produce the rhombus.FIG. 5E depicts that two triangles of infinite height with orthogonalsides produce the rectangle sub-class of parallelogram. FIG. 5F depictsthat generating triangles with orthogonal pairs of parallel sides andequal bases produce the square.

FIG. 6 depicts a convex, quadrangular target with apexes at 624, 660,650, and 610. For purposes of developing the logic of the presentinvention, the origin of the coordinate system is made to coincide withone external apex and the X-axis aligned with the bisector of this apex.In FIG. 6 this is apex 600 with its bisector being 644.

Define the "Primary Triangle" to be the generating triangle having itslargest inscribed circle also inscribed in the quadrangular target.Specifically, the primary triangle is that triangle of the twogenerating triangles having the largest inscribed circle of leastradius. The non-primary generating triangle will be termed the"Secondary Triangle." The physical target contains two apexes which arealso apexes of the primary triangle. These will be termed "Base-Apexes".The target also contains two apexes which are not apexes of the primarytriangle. These are termed "Nonbase-Apexes".

Analysis of quadrilateral targets proceeds by recalling that the slopeof a line ab defined by any two points, "a" and "b", on a Cartesiancoordinate system is: ##EQU33## with its length defined by Eq. 2.

The equation of the family of parallel lines defined by two points, "a"and "b", is defined: ##EQU34## with the specific equation of the line,ab, expressed as: ##EQU35##

Also required for the analysis of quadrilateral targets is determinationof the intersection of two non-parallel lines. To this end, consider anadditional line defined by points "c" and "d" having slope S_(cd)≠S_(ab). The intersection of lines ab and cd is determined by:

    y.sub.a +S.sub.ab (x-x.sub.a)=y.sub.c +S.sub.cd (x-x.sub.c)

which after rearranging terms gives:

    x=-k(y.sub.a -S.sub.ab x.sub.a)+k(y.sub.c -S.sub.cd x.sub.c)(Eq. 11)

where: ##EQU36## Solving for y: ##EQU37## The result is:

    y=-kS.sub.cd (y.sub.a -S.sub.ab x.sub.a)+kS.sub.ab (y.sub.c -S.sub.cd x.sub.c)                                                  (Eq. 12)

From geometry it is known that the center of the largest circle tangentto three lines intersecting at two points, "g" and "j" is theintersection of the lines bisecting angles formed at points "g" and "j".To find this intersection assume an arbitrary line hg is defined by(x_(g),y_(g)) and (x_(h),y_(h)). Define "α" as the angle between thex-axis and line hg: ##EQU38## Similarly, define β as the angle betweenthe x-axis and a second arbitrary line, jg, which intersects line hg:##EQU39## Define δ to be the angle relative to the x-axis of the linebisecting angle ∠hgj: ##EQU40## Utilizing Eq. 10, the equation of thebisector of the angle formed by the lines hg and gj; namely, gB_(g) is:

    y=y.sub.g +S.sub.gB.sbsb.g (x-x.sub.g)

where: ##EQU41## The equation for a second angle bisector may berepresented as: y=y_(j) +S_(jBj) (x-x_(j)). From Eq. 11 and Eq. 12, wecan express the intersection of bisectors of two adjacent apexes of apolygonal target as: ##EQU42## Define the "Largest Inscribed ExtremeCircle" to be the largest circle that can be inscribed within thephysical target that has tangency with three sides of the physicaltarget. To identify the largest inscribed extreme circle of an arbitraryquadrilateral target apply Eq. 13, Eq. 14, and Eq. 15 to determine theintersection of the bisectors of the two base-apexes of the primarytriangle. The radius of the largest inscribed extreme circle is thelength of the normal line from the intersection of the above determinedbisector intersection to a nearest side of the quadrilateral, a distancedetermined by application of Eq. 2, Eq. 3, and Eq. 4.

To illustrate these concepts, in FIG. 6 the center of the largestinscribed extreme circle is depicted as location 654; i.e., theintersection of bisectors 640 and 648 of base apexes 660 and 650respectively. The radius of this circle is the length of the normal from654 to a nearest side of the quadrilateral; say the side 606. This isline 656. Employ Eq. 4 to determine the length of line 656; i.e.,∥656∥=X_(m) sin θ where θ is angle 604.

Similarly, define the "Smallest Inscribed Extreme Circle" to be thesmallest circle which can be inscribed within the target having tangencywith three sides of the target. To identify the smallest inscribedextreme circle of an arbitrary quadrilateral target apply Eq. 13, Eq.14, and Eq. 15 to the intersection of the bisectors of the two non-baseapexes. The radius of the smallest inscribed extreme circle is thelength of the normal line from the intersection of the above determinedbisector intersection to a nearest side of the quadrilateral, a distancedetermined by application of Eq. 2, Eq. 3, and Eq. 4. For FIG. 6, theintersection of bisector 642 of non-base apex 624 and bisector 646 ofnon-base apex 610 define the center, 618, of the smallest inscribedextreme circle 638. To prove this, note that in FIG. 6 r₁ n⊥JK and r₂n⊥KH due to tangency conditions and that ##EQU43## because they areradii of the same circle. Since ##EQU44## line kn bisects ∠JKH. Itfollows that ΔKr₁ n=ΔKr₂ n since triangles having three equal angles anda common side are equal. Similar logic shows that point n falls on lineHB_(H) , the bisector of ∠KHG. This proves that the center, n, ofsmallest extreme inscribed circle falls on the intersection of thebisectors of the external apex and non-base apexes ∠JKH and ∠KHGrespectively. The length of the radius of the smallest inscribed circleR_(N) is determined from Eq. 4; i.e., ##EQU45## The intersection of thebisector, QB_(Q) of angle ∠JQG, and the bisector of either of thenon-base apexes also determines the center, n, of the smallest inscribedextreme triangle. We know that r₁ ⊥JQ and nr₃ n⊥QG from tangencyconditions and that ##EQU46## because both are radii of the same circle.With Qn common to ΔQr₁ n and ΔQr₃ n, we have: ##EQU47##

It can be noted that the radius of the smallest inscribed extreme circlecan equal the radius of the largest inscribed extreme circle only whenthe there is a single infinite external apex as with the trapezoid orwith quadrilaterals having (X_(n),0)=(X_(m),0).

Once the primary triangle is identified, analysis applies solely to theprimary triangle. Once the acquiring entity position is determinedrelative to the MaxETL's quadrilateral target analysis is identical totriangle target analysis when the initial acquiring entity location is:(1) not within any region delimited by the three MaxETLs of the primarytriangle, (2) within a region delimited by one of the four MaxETL of thequadrilateral's apexes, (3) on any ETL containing the external apexhaving an intersection between said ETL and the line segment defined bythe centers of the smallest and largest inscribed extreme circles. Forinitial acquiring entity positions located on ETLs containing theexternal apex and an intersection between said ETL and the line segmentdefined by the external angle's apex and the center of the smallestinscribed extreme circle, the optimum target acquisition point is thecenter of the smallest inscribed extreme circle.

The exemplar quadrilateral of FIG. 7 illustrates application of theseresults. For initial acquiring entity locations more distant from thecenters of the MaxETL of the primary triangle than the radii of saidMaxETL, the acquiring entity is located within the 746 region. As shownduring analysis of the triangular target, the optimal traverse from thisregion is to 756, the center of the largest inscribed circle . Initialacquiring entity locations not within the 746 region are within theinfluence of one of the apex ETLs. To identify the relevant apex,iterate to compare the distance from the acquiring entity to the centerof each apex MaxETL to the radius of said apex MaxETL. If the MaxETL ofone of these apexes contains the initial acquiring entity location, theaxis is transformed to produce the environment of FIG. 3 and theanalysis developed for apex ETL analysis applied. If the preceding doesnot identify a MaxETL containing the acquiring entity location, theacquiring entity is located within the MaxETL of the external apex.Since the optimal traverse from acquiring entity locations within the708 MaxETL that are more distant from 706 than ##EQU48## will terminatewithin the quadrilateral, they are analyzed in the manner described fortriangular analysis. Initial acquiring entity locations less distantfrom 724 than ##EQU49## have the smallest inscribed extreme circle asthe implicit target. Analysis of Rectangular Targets

FIG. 5E indicates that a rectangular target is defined by two generatingtriangles, each with infinite external apexes and having orthogonalsides. The primary triangle is the generating triangle having thenarrowest base. With the diameter of all inscribed circles being equal,minimization of ##EQU50## is attained by minimization of D_(t).

When the initial acquiring entity location is within a MaxETL region theoptimal traverse is determined by applying the apex ETL analysisintroduced during analysis of the triangular target. For other locationsit can be shown that if the line segment defined by the centers of theinscribed extreme circles can be reached via a normal traverse, thenormal traverse is the optimal traverse to the target. For all remaininginitial acquiring entity locations the optimal traverse is to thenearest inscribed extreme circle.

To elucidate, consider that if in FIG. 8 the infinitely remote externalapex is at -X.sub.∞, 848 denotes the ETL of infinite radius whichcontains the center of the right-most inscribed extreme circle. Fromgeometry of the target and the extreme inscribed circle it is apparentthat ##EQU51## am⊥mb and the shape maJb forms a square. mJ and ab arediagonals of square maJb and are thus of equal length and intersect atright angles. Since the hypotenuse of right triangle ΔaJb is a diagonalof 854, point a is the intersection between physical target side KJ, theMaxETL of the infinitely remote external apex, and the MaxETL containingpoints m and J. Parallel arguments hold for remaining apexes of thephysical target. It is thus concluded that if a normal traverse to theline segment between the centers of inscribed extreme circles ispossible, it is not possible for this initial acquiring entity locationto be located within a region bounded by the MaxETL of a physical targetapex.

FIG. 8 depicts a rectangular target of Aspect Ratio>>1 having acoordinate system with origin at the target's center-of-gravity andX-axis coincident with the target's horizontal center line. Consider 806and 848 to be ETL's of the infinite external apex located to the leftand passing through the centers, 816 and 858, of inscribed extremecircles 818 and 862 respectively. If coordinates of the acquiring entityare designated by (X_(c),Y_(c)), preceding results permit the conclusionthat if 806_(X) ≦X_(c) ≦848_(X) the acquiring entity cannot be locatedwithin any of the MaxETLs. For analysis of rectangular targets thefollowing three step procedure is the preferred approach:

1) Case of: (848_(X) <X_(c))

a) If the acquiring entity location lies within either the 854 MaxETL or868 MaxETL translate the acquiring entity and pertinent apex to producethe alignment depicted by FIG. 3 and determine the optimum hit locationusing Eq. 6.

b) If the acquiring entity does not lie within either the 854 MaxETL orthe 868 MaxETL, select point 858 as the optimal hit location.

2) Case of: (806_(x) ≦X_(c) ≦848_(x)). Select point (X_(c),0) as optimumhit location.

3) Case of: (X_(c) <806_(x))

a) If the acquiring entity location lies within either the 808 MaxETL orthe 824 MaxETL, translate the acquiring entity and pertinent apex toproduce the alignment depicted by FIG. 3, determine the optimal hitlocation using Eq. 6.

b) If the acquiring entity does not lie within either the 808 MaxETL orthe 824 MaxETL, select point 816 as the optimum hit location.

These results are paralleled for rectangular targets with AR<<1 sincesuch a target can be rotated 900 to produce the environment of FIG. 8,thus permitting application of previous analysis

DETAILED DESCRIPTION OF THE INTERFACE GRAMMAR

The InterFace Grammar

Procedures presented below have ancestry in the Goals, Operators,Methods, and Selection (GOMS) model (Card, S., Moran, T., and Newell,A., The Psychology of Human-Computer Interaction, 1983) and subsequentlyappraised with qualified results as an interface design tool by Poison(Poison, P. A Quantitative Theory of Human-Computer Interaction, inCarroll, J., (ed.) Interfacing Thought: Cognitive Aspects ofHuman-Computer Interaction, 1987, pp. 184-235), (Karat, J. and Bennett,J., Working Within the Design Process: Supporting Effective andEfficient Design, in Carroll, J., (ed.) Designing Interaction:Psychology at the Human-Computer Interface, 1991, pp. 269-285), andTetzlaff, L. and Mack, R., Discussion: Perspectives on Methodology inHCl Research and Practice, in Carroll, J., op. cit., 1991, pp-286-314).While this invention employs the concept of subdividing user activityinto sequences of subgoals and activities as pioneered by GOMS, itdiffers from GOMS by not seeking to predict periods during which usersengage in cognitive activity and by not seeking to predict overt userbehavior during evaluation of existing interfaces.

For purposes of developing this section, it is presumed a computer-humaninterface is designed to control the functionality of an applicationsystem as specified by an explicitly or implicitly developedRequirements Specification; a document whose preparation and purpose arewell understood by those experienced in the art. It is also presumedthat data to permit comparison of the computer-human interfaces beingevaluated by the invention derive from explicit or implicit performanceof a standard task suite reflective of typical use of the said comparedapplication software. It is finally presumed that input-output devicesavailable to the user are the keyboard, mouse, trackball, joystick andCRT, operation of which entails performing the following physicaloperations: single key stroke, multi-key stroke, cursor move, cursordrag, button click, button multi-click, hand-homing, and finger-homing.

Define a "Terminal Session" to be the sequence of physical operationsundertaken by users on input devices of a computer-human interface whileaccomplishing the standard test suite. It is posited that during aterminal session the user seeks to accomplish some primary goal, P,which is subdivided into a set of subgoals, G₁, . . . , G_(k), thataccomplish P. The invention additionally posits that software designersmust provide at least one method, M, with which to accomplish eachsubgoal. A method comprises one or more tasks, T, performed by the userthat, when successfully performed, parameterize software functionalitythat accomplishes the subgoal of said method. To accomplish each task ofa given method the user executes a sequence of one or more of the abovespecified physical operations, O, on the input devices. Stated formally,the invention defines a terminal session to be the performance of a setof methods, M_(a), 1≦a≦b, which accomplish the k subgoals, G_(i), 1≦i≦k,into which the primary goal, P, is decomposed. Each method, M_(a),comprises a set of one or more tasks, T_(d), 1≦d≦e. Each task of eachmethod comprises an ordered sequence of one or more physical operators,O_(j). . . O_(l), that conform to the syntactic rules defined for thesoftware during its design. A terminal session is thus comprised of atemporally ordered sequence of physical operations in which subgoal 1 isachieved before subgoal 2, etc., thus: ##STR1## where: P the primarygoal.

G_(i) a subgoal; i.e., a subdivision into which the user partitions P.

M_(a) a method; i.e., a process activating functionality to accomplishG_(i)

T_(d) a physical task; i.e., one or more physical operations thatparameterize each component of M_(a).

O_(c) a physical operation.

Performance of each T_(d) entails acquisition of at least one target,the acquisition of said target entailing traversing a distance D_(t) toacquire a target of width W_(t) which, provided defensible values forD_(t) and W_(t) exist, entails expending ##EQU52## bits of effort.Aggregating the physical effort expended to execute the individualphysical operators provides a measure of the total physical effortembodied in a terminal session, thus: ##EQU53## where: l_(T) totalphysical effort expended.

M_(a) the a^(th) in a sequence of b methods which accomplish P.

T_(ad) the d^(th) in a sequence of tasks forming the a^(th) method.

l(O_(adc)) the physical effort expended to perform the c^(th) physicaloperation of the d^(th) task of the a^(th) method executed.

Application of this result to interface evaluation entails a symbologywhich permits description of all displayed, targetable screen graphicsand all user activity performed on input devices during a terminalsession. In particular, capabilities of said symbology comprise: (1)specification of location, shape and size of any targetable artifact ofthe computer-human interface irrespective of whether said targetableartifact is a component of the system supplied Graphic User Interface ora component of the application system, (2) management of alterations tosaid targetable artifacts by the user, (3) specification of text orpattern fill of targetable artifacts enabled to receive fill, (4)ability to render visible or non-visible any targetable artifact, (5)ability to set defaults appropriate to terminal session needs, and (6)specification of linkages in which user manipulation of one targetableartifact induces secondary effects to one or more other targetableartifacts. The InterFace Grammar (IFG) presented in Appendix A is asymbology addressing these requirements expressed via Backus-Nuar Form(BNF), a notation well understood by those skilled in the formallanguage arts. BNF specifies syntax rules in the formTERMINAL/NON-TERMINAL<NON-TERMINAL whereby any embedded substring ofnon-terminal symbols matching the left-hand side of a Backus-Nuar Formproduction can be replaced by any substring on the right-hand side ofsaid production. In addition to detailing productions which delimitphysical operations of individual methods, declare default values, andprovide other ancillary artifact management, the BNF notation appearingin Appendix A details the two separate but inter-related divisions ofthe InterFace Grammar (IFG). The Graphic-User-Interface Descriptor(IFG/GUID) detailed in Appendix A by the section "Grammar to Describethe Graphic User Interface" presents an extensive but non-exhaustiveIFG/GUID which is here included to make possible the example presentedbelow. The IFG/GUID is not considered part of the present invention. Thesecond major IFG division is the Physical Operation Descriptor (IFG/POD)and is detailed in Appendix A by the sections "Grammar for PhysicalOperations Performed of the Keyboard" and "Grammar for PhysicalOperations Performed for Cursor Control." The IFG/POD presents BNFproductions permitting exact description of actual or predicted usermanipulation of input devices undertaken to accomplish the primary goalof a terminal session. IFG/POD code is employed in conjunction withIFG/GUID or its equivalent too objectively identify the implicit targetwhich minimizes physical effort expended to acquire each physical targetgiven an arbitrary initial location of the acquiring entity. Thiscapability permits objective, quantitative determination of the physicaleffort expended during target acquisition. Not being obvious to personsof normal skill in the prior art of computer-interface design,procedures which utilize the Physical Operation Descriptor of theInterface Grammar are considered a component of the present invention.

For IFG/POD and IFG/GUID to be applicable to quantification of thephysical effort of manipulating a computer-human interface it must bepossible to declare system default values. IFG/POD and IFG/GUID syntaxfor system default specification is:

\D KEYWORD=keyword-value!

\D commences an IFG sequence that defines a system default production."KEYWORD" represents a reserved word denoting a parameter."Keyword-value" is a system suggested value, a selection from IFGprovided values, or a user supplied value.

IFG/GUID syntax for specification of key location on the keyboard is:

    ______________________________________    \B KEYBOARD=    START,    UNITS={xx},    KEYSIZE={h,w},    KEY={key identification}, LOCATION={x,y},    KEY={key identification}, LOCATION={x,y},    ...    END!    ______________________________________

"\B" commences an IFG sequence to define key locations while "START" and"END" bound the series of specifications defining size and location ofeach key of the keyboard. "KEY" identifies the key(s) being describedand permits their assignment to alphameric, general function,pre-defined function, cursor control, toggle or numeric pad categories."LOCATION" either explicitly designates or permits determination of thelocation of each key.

Within IFG/GUID artifacts are categorized either as classes andstructures or as objects and associations. Classes are abstracttemplates from which individual objects are instantiated to representindividual, real-world concepts being manipulated by the applicationsoftware. Structures are abstract templates from which aggregations ofartifacts are instantiated to represent complex, real-world conceptsbeing manipulated by the application software. IFG/GUID syntax generallyconforms to one of the following formats:

    ______________________________________    \GC CLASS=tag.sub.c, SHAPE=type(apexes),/PARMS!    \GS STRUCTURE=tag.sub.s, {object/association list}, /PARMS!    \GO OBJECT=path<tag.sub.o >, CLASS=tag.sub.c,    LOCATION=(x,y),/PARMS!    ______________________________________

\GA ASSOCIATION=path<tag_(A) >, STRUCT=tag_(s), LOCATION=(x,y), /PARMS!"\Gx" commences an IFG/GUID symbol string that defines a screen artifactof type "x"; "x" denoting a class, structure, object, or association."Path" appears for Object and Association artifacts to identify the datastructure providing the coordinate system of artifacts being defined."Location" applies to Objects and Associations to specify eitherpositioning of the artifact being referenced or the coordinates to whicha previously acquired artifact is to be moved. "Tag" provides names toindividual artifacts or to sets of undifferentiated artifacts beinggenerated to permit specific artifact identification during subsequentmanipulation. "Parms" either explicitly or implicitly declare parametersappropriate to control of a particular artifact or class of artifact.

IFG/POD permits specification of each user action that manipulates aninput device of the human-computer interface. IFG/POD syntax forspecification of physical operations on the keyboard is:

"\Kx{sequence of one or more key strokes}

"\K" commences an IFG keying sequence with "x" denoting one of thefollowing category of key: alphameric, general function, pre-definedfunction, cursor control, toggle, or numeric pad.

Generally IFG/POD syntax for specifying physical operations of cursormanagement is:

\C{function activation}{target acquisition}{function activation}

Curly brackets, "{. . .}", denote optional physical operations performedin a manner specified by interface designers. When the syntax denotesfunction activation reference is to permitted button manipulation or tosimultaneous button and keyboard manipulation. "Target acquisition"either references traverse to an extant graphic artifact or designatestraverse to a location in white-space. IFG/POD syntax for cursormovement is:

path<tag>(segment or location or unbounded target)

"Tag" is the unique name of a displayed physical target to be acquiredwith its point of acquisition specified relative to the axis system ofthe ancestor association of which "tag" is a member. "Segment" denotesthe component of the physical target such as the middle, an edge, orcomer to be acquired. "Location" applies to targets not having uniqueidentification that are acquired by delimiting an area of non-targetreal-estate within the "parent." association that contains the desiredtargets. Text strings and simultaneous acquisition of multiple artifactsexemplify such targets. An unbounded target is acquisition of an areanot explicitly delimited by a physical target that is to be visualizedas a circular area having radius dependent on the precision required toaccomplish the purpose of performing the current task.

Since exigencies of a particular application may require adjustment tothe capabilities of the IFG/POD that are not explicitly detailed inAppendix A, the invention encompasses such adjustments as are in keepingwith the spirit and purpose of the Physical Operator Descriptorproductions of the InterFace Grammar. Additionally, whereas BNF is onemethod with which to express a computer-human interface and usermanipulation conducted thereon, it is realized that alternate methodsfor expressing the purpose of the Physical Operator Descriptor aspectsof the InterFace Grammar are available which are equally applicable. Itis the spirit and purpose of a symbology designed to permit descriptionof a computer-human interface and physical operations thereon with theintent of determining the physical effort incurred during a terminalsession that is considered within the scope of this invention. Inconsequence, the validity of the IFG/POD aspect of the present inventiondoes not depend on a particular style and form of symbology.

AN EXAMPLE ILLUSTRATING IMPLEMENTATION OF THE INVENTION

This section introduces the environment of a computer based activity,presents specifications of a standard test suite, and summarize resultsfrom application of the physical effort metric. The next page presentsthe specifications for an exemplar application of the physical effortmetric with interpretation of results presented on subsequent pages.FIG. 9A through FIG. 9T present detail of procedures followed to achievethese results.

    ______________________________________    Exemplar Standard Task Suite: Assumptions and Specifications    ______________________________________    Assumptions of the Example:    1.  Comprehension of the InterFace Grammar of Appendix        A is presumed.    2.  FIG. 9A presents the GUI assumed for this example.        Artifacts are drawn to scale with artifact origins        presented relative to the origin of their parent association.        Measurement is in inches.    3.  The GRABWIDTH parameter is 2 pixels; i.e. +0.014 inches.    4.  Four strategies for performing the Standard Test Suite are        illustrated    Drop-Down Menu Bar:                      Depicted by FIG. 9M and FIG. 9N    Icon Activation:  Depicted by FIG. 9O and FIG. 9P    Pop-Up Spider Menu:                      Depicted by FIG. 9Q and FIG. 9R    (Description of the Spider Menu appears in Appendix B)    Cmd-Key Equivalent:                      Depicted by FIG. 9S and FIG. 9R    5.  The terminal session commences with the cursor located at "+".    6.  Cursor traverses are depicted in order of occurrence via        T1, T2, . . ., Tn.    Specifications of the Standard Test Suit:    Subgoal 1:           Delete the trapezoidal target.    Subgoal 2:           Set to bold the text string "receive some           bold font"    Subgoal 3:           Cut the complete text string "This is a           string . . . before paste." and paste it over the           quoted text string "indicated here."    Subgoal 4:           Perform one-dimensional scaling of the standard           rectangle by displacing the left edge (-0.9 ± 0.014) inch.    Subgoal 5:           Move the triangular target 1.36 inches left and 0.76           inches upward.    Subgoal 6:           Perform two-dimensional scaling of the circular target           by placing the bottom-left corner at location ((7.60,           5.50) ± 0.014) inch.    ______________________________________

FIG. 9A displays the CRT environment for a basic GUI with its canvaspre-populated by artifacts specified by the test suite. Coordinatelocations shown are specified in the manner supported by the IFG/GUID ofAppendix A; namely, coordinate values of an artifact are specifiedrelative to the parent association of the artifact referenced. Thus, theorigin of the "Edit" option of the menu is location (1.3, 0.0) relativeto (0.1,0.5), the origin of the menu association which itself isrelative to (0.0,0.0), the origin of its parent Window association.Similarly, "Cut", an element of the "EditStru" structure, has (0.0,0.9)as its origin expressed relative to its parent reference of (1.3,0.0),the origin of the object "Edit."

FIG. 9B through FIG. 9E present IFG code that specifies: (1) defaultvalues, (2) IFG/GUID code declaring a window, a drop-down menu bar,icons, and a port association comprising scrollbars, viewport, and (3)IFG/GUID code depicting application system objects populating thecanvas. information required for IFG/GUID coding of the GUI is generallyenvisaged to be a schematic detailing size, location of the GUl'sartifacts and transforms permitted to their graphic display. IFG/GUIDcode to depict artifacts of the test suite derives from specificationsof the standard test suite. In the present example, IFG/GUID code isemployed to populate the canvas prior to performing the test suite whichhas as its primary goal the editing of six pre-existing graphic objects.Another test suite may entail user activity which includes populatingthe canvas.

Materials of FIG. 9F through FIG. 9K are not subsumed within the presentinvention since these materials are well understood by practitioners ofthe interface design arts. These sheets are included only to illustratethe process whereby METHODs and TASKs produce the IFG/POD strings thatdescribe the physical operations of a terminal session and how theseIFG/POD strings are subsequently utilized to quantify the physicaleffort of performing the standard test suite. FIG. 9F and FIG. 9Gillustrate a set of TASKs which can be variously combined to produce theset of METHODS presented by FIG. 9H through FIG. 9K. Each task specifiesa header and a set of explicit physical operations to be performed bythe user. A TASK-HEADER receives a user supplied name to identify boththe type of physical target impacted by the task and the manipulationperformed on that target. The ACTION component of the TASK-HEADERcategorizes the particular manner in which each task performs the saidmanipulation. The combination of task-name and task-action must combineto form a unique phrase to permit its identification. Task-headersadditionally include one or more formal ARGS to provide the task withgeneric characteristics that permit reusability.

FIG. 9H through FIG. 9K illustrate a set of seventeen METHODS; eachdefined to accomplish one subgoal of the test suite. The seventeenmethods presented, formed by variously combining the thirteen tasks ofFIG. 9F FIG. 9G, illustrate that a CHI provides multiple methods forperforming each subgoal of a terminal session. While naming conventionsare similar to those employed for naming tasks, method names explicitlydesignate the artifact to which the method applies and the subgoal itaccomplishes. The STYLE qualifier provides a designation to suggest thedominate technical approach employed by the method.

When the invention is employed to assist designers it is presumed astatement of desired functionality exists and the invention is employedto help determine icon size and position, consistent button usage,optimal menu style, key-equivalent bindings, etc. During design all suchdecisions become variables of the formal argument lists of the methodset being developed. When the invention is employed to evaluate aninterface, it suffices that only user emitted actions be entered asparameters into the method's formal argument list since parameterspre-defined during design are known to the method. FIG. 9L illustrateshow a method is coded and its task set parameterized to accomplishsubgoal 3 of the test suite via the spider-menu approach (see AppendixB, FIG. 9Q, FIG. 9R, and FIG. 17 for detail of the spider menu). Uponuser activation top-level options in spider menu format are displayedwith the cursor positioned by program control at the center of thedisplay. To affect a selection the user traverses the cursor in a radialdirection into the desired option and clicks the left button. If thereexists a sub-menu option of the selected option the system displayssecond level options appropriate to the selected top-level option.Selection of a leaf option results in deletion of the menu graphic withthe cursor generally returned to the location occupied prior to menuactivation.

Physical operations performed by the user to accomplish the standardtest suite in a manner to maximize use of the drop-down menu system aredetailed by FIG. 9M. The cursor is initially located at coordinates(4.73,4.08) expressed relative to the origin of the Port association,The subgoal of trapezoid deletion is accomplished via the"Target-Delete/MenuBarSel" method. FIG. 9N shows that this methodentails a cursor traverse along the T1 path into the middle of thetrapezoid, a left button click, a traverse along path T2 into the "Edit"option of the menu bar, another left-button click, a traverse of path T3into the "Cut" sub-option of "Edit", and a final left button click.Successive tasks proceed in similar manner. The "IFG" entry undersubgoal 1 of FIG. 9M presents the InterFace Grammar code specifying thissequence of user activity. The "Effort" entry indicates physical effortexpended to accomplish these individual operations and the aggregate forthe complete method. The remainder of FIG. 9M details the completesequence of methods selected to perform the standard test suite usingdrop-down menu bar when appropriate, the IFG physical operationsexecuted during performance of each method, and the physical effortsexpended. FIG. 9N displays the complete sequence of moves and implicittargets acquired when accomplishing the standard test suite using thesaid drop-down menu bar. Subsequent pages of FIG. 9 presents terminalsession histories and subsequent analysis for icon, spider menu andkey-equivalent approaches to performing the standard test suite.

The following table displays results of physical effort expended duringperformance of the example's standard test suite in both absolute termsand in terms relative to the key-equivalent technique. Thekey-equivalent technique is employed as the base for relative comparisonas this technique is generally considered by those knowledgeable incomputer usage to require least physical effort to accomplish a subgoal.Since each terminal session of the example entails identical physicaloperations for Subgoals 4-6 of the example, the physical effort incurredfor their attainment is identical. With one-half of the physicalsubgoals for each terminal session being of identical physical effort,the drop-down menu bar requires 26 more percent physical effort overallthan does the key equivalent approach. The icon approach requires 10percent more physical effort and the spider menu technique requires 13percent less. When only subgoals employing different approaches tosubgoal accomplishment are compared the drop-down, the icon and thespider menu approaches entail 145, 118 and 79 percent the physicaleffort relative to the key-equivalent approach. With this example allsubgoals of the test suite can be achieved via menu or icon based styleswithout hand homing while with the key-equivalent approach hand homingfrom keyboard to mouse and back is required, In consequence, thisexample may not fully reflect typical real-world terminal sessions andthus somewhat biased in favor of menu/icon based methods. Irrespective,the example suggests that prevalent styles of menu design provided bycurrent commercial GUIs are inefficient relative to alternate menustyles. This conclusion is concordant with results of an unpublishedexperiment which investigates the efficacy of different menu designsconducted in support of U.S. patent application Ser. No.

    ______________________________________    Results of Applying the InterFace Grammar to Evaluate the    Physical Effort of Various Terminal Sessions    (see FIG. 9 for detail)    Drop-Down                Spider    Key-    Menu           Icon      Menu      Equivalent            Total          Total     Total     Total    Subgoal bits    Ratio  bits Ratio                                     bits Ratio                                               bits Ratio    ______________________________________    Delete Obj.            9.84    1.40   7.35 1.05 5.34 0.76 7.04 1.00    Bold Text            15.23   1.27   13.02                                1.08 9.79 0.81 12.04                                                    1.00    Cut-Paste            31.78   1.57   25.97                                1.29 15.86                                          0.78 20.21                                                    1.00    X-Scale 11.22   0.99   11.25                                0.99 11.38                                          1.00 11.38                                                    1.00    Move Object            3.99    1.00   3.99 1.00 3.99 1.00 3.99 1.00    X,Y-Scale            11.97   1.00   11.97                                1.00 11.97                                          1.00 11.97                                                    1.00    TOTAL   84.03   1.26   73.55                                1.10 58.23                                          0.87 66.63                                                    1.00    ______________________________________

The example suggests that results generated by the quantitative,objective procedures embodied in the present invention correlate withthe consensus of persons experienced with computer usage regardingrelative levels of physical effort expended when using differingapproaches to interface manipulation. The example also suggests thatdifferences in physical effort of method execution can be substantialthus justifying attention to its reduction through design evaluated bythe present invention.

ENVIRONMENT FOR APPLICATION OF THE INVENTION

Practical implementation of the invention presumes that IFG sequences ofa terminal session are generated via software that offers apseudo-natural language and palettes of graphic objects suitable forexpressing the GUI environment and define methods of the applicationsoftware undergoing evaluation. Being neither integral to the presentinvention nor an addition to the computing arts for those of normalskill, only the purpose and results of these software capabilities arehere described.

Support Environment for the Design of Interfaces

FIG. 10A depicts an environment appropriate to application of theinvention as an aid to the design of interfaces for a proposed softwaresystem. Preliminary to employment of the invention task analysis, 10100,is performed to identify the functionality to be provided by thesoftware and the input-output requirements. Also preparatory toemployment of the invention is activity to ascertain the software'stypical application. Resulting is a set of representative tasks whichbecome the test suite of standard activities 10104. If exigencies of aparticular application require, the two components of the InterfaceGrammar, 10102 and 10114, are adapted prior to the drafting of methods.Once method drafting is complete, there will exist one Graphic-UserInterface, 10106, and one set of methods, 10108, for each proposedinterface.

Application of the invention commences after completion of these stages.Initially, IFG/GUID descriptions of the keyboard and artifacts of eachGUI proposed are produced 10102. It is presumed there is available oneor more persons with skills appropriate to each proposed interfacedesign. These persons devolve the primary goal of accomplishing the testsuite into subgoals ordered in the sequence performed within aproduction environment. A proposed CHI is selected and the mostappropriate method, 10110, of accomplishing each subgoal identified.

Each method and target(s) selected is then expressed to the inventionvia an Interface Pseudo-Code, 10112. Whereas in one aspect the inventionpertains to identification of the physical subset of points usersidentify while acquiring an arbitrarily shaped and located triangular orquadrangular target, actual identification of the physical points whichcomprise the implicit target entails aspects of the invention burdensomefor the designer to apply using manual techniques. The InterfacePseudo-Code exists to permit users to describe the real-worldenvironment they confront in a minimally burdensome manner. When theInterface Pseudo-Code is an integral component of the interfaceevaluation system, the Interface Pseudo-Code translator 10116 thatparses the pseudo-code into IFG/POD symbols, 10114, will be programmedto maintain data structures which store parameters defining the currentstatus of each interface target. Output of 10116 is an ordered set ofInterface Grammar symbols which comprise the Terminal Session Record,10120. Submitting 10120 to analysis by the physical effort procedure,10122, produces metrics showing physical effort expended during aterminal session that uses a given CHI, 10124. This process is repeatedfor each proposed interface and results in one report of inferredphysical effort expended during a terminal session using a proposedcomputer-human interface.

Support Environment for Evaluation of Existing Interfaces and ComputerUsers

FIG. 10B depicts the environment typical for application of theinvention to either evaluation of existing interfaces or to evaluationof personnel. Preliminary to employment of the invention, the software'stypical application, 10200, is ascertained and a set of representativetasks identified which define the test suite of standard activities,10202.

Application of the invention now commences. It is presupposed there isavailable one or more persons with skills appropriate to each of theinterface designs undergoing evaluation; i.e., knowledgeable regardingthe implications of 10204 and 10214 without actual knowledge of IFGitself. These persons accomplish 10208; i.e., physically perform thestandard test suite using each interface being evaluated. For eachinterface all physical operations performed by the user while performing10202 are recorded either through direct electronic event capture orthrough video recording of each terminal session, as indicated by 10210.When event capture is employed, the event queue of the computer'sgraphic user interface is screened for entries pertaining to targetacquisition and relevant events are converted into symbol sequences ofthe Interface Grammar. When video recording of user activity isemployed, the video record is viewed, the physical operations performedare identified, and each physical operation expressed via InterfacePseudo-Code. Upon parsing the Interface Pseudo-Code, 10216, there existsa Terminal Session Record, 10222, which details each physical operationperformed on each interface during performance of the test suite ofstandard tasks. Submitting 10222 to analysis of the invention, 10224,produces metrics showing actual physical effort expended during aterminal session using a given CHI, 10226.

DETAILED DESCRIPTION OF IMPLICIT TARGET ANALYSIS

Notation and Definitions

It is above noted that the mathematical arts commonly identify areferenced entity via a base symbol with attribute identification ofsaid entity achieved by subscripts, superscripts and other forms ofsymbol attached to the base symbol. Employing this convention, thefollowing list presents definitions and notation utilized bymathematical references employed during the detailed description of thepresent invention:

    __________________________________________________________________________    Definition                  Notation    __________________________________________________________________________    Reference to acquiring entity                                C    Reference to arbitrary apex of the physical target                                A    Coordinates of arbitrary apex of the primary generating                                (X.sub.A, Y.sub.A)    Reference to external apex of the primary generating triangle                                E    Coordinates of external apex of the primary generating triangle                                (X.sub.E, Y.sub.E)    Reference to largest inscribed circle identified by base-apexes                                M    Reference to center of M    m    Coordinates of center of M  (X.sub.m, Y.sub.m)    Radius of M                 R.sub.M    Reference to largest inscribed circle identified by nonbase-apexes                                N    Reference to center of N    n    Coordinates of center of N  (X.sub.n, Y.sub.n)    Radius of N                 R.sub.N    Reference to implicit target                                T    Reference to center of T    t    Coordinates of center of T  (X.sub.t, Y.sub.t)    Radius of T                 R.sub.T    Reference to arbitrary Equi-Target Loci through apex A & point                                ETL.sub.Az    Reference to center of ETL.sub.Az                                etl.sub.Az    Coordinates of center of ETL.sub.Az                                (X.sub.etl.sbsb.Az, Y.sub.etl.sbsb.Az)    Radius of ETL.sub.Az        R.sub.ETL.sbsb.Az    Reference to Max Equi-Target Loci through apex A & point                                MaxETL.sub.Az    Reference to center of MaxETL.sub.Az                                max etl.sub.Az    Coordinates of center of MaxETL.sub.Az                                (X.sub.maxetl.sbsb.az, Y.sub.maxetl.sbsb.Az)    Radius of MaxETL.sub.Az     R.sub.MaxETL.sbsb.Az    Coordinates of arbitrary point Z                                (X.sub.Z, Y.sub.Z)    Reference to line between points Z.sub.1 and Z.sub.2                                L.sub.Z.sbsb.1, .sub.Z.sbsb.2    Length of line between points Z.sub.1 and Z.sub.2                                ||L.sub.Z.sbsb.1,                                .sub.Z.sbsb.2 ||     ##STR2##                   D.sub.t    Width of Implicit Target (W.sub.t = 2 × R.sub.T)                                W.sub.t    Index of Difficulty formulated from D.sub.t and W.sub.t                                I.sub.t    __________________________________________________________________________

Given that many references in the detailed description of the presentinvention relate to attributes of geometric objects, comprehension ofthe detailed description is increased through figure references thatidentify the uniqueness if each entity referenced while concomitanlycommonalties within a given figure and between different figures. Thefollowing convention for FIGS. 12 through 16 is employed:

FPea

where:

F→symbols 12 through 16 identify the Figure referenced.

P→as appropriate, symbols A through H identify the Part of Figure Freferenced.

e→symbols 0-9 identify a referenced artifact of Figure F Part P.

a→symbols 0-9 identify a referenced attribute of Artifact e of Figure FPart P.

    ______________________________________    "e" assignment:     e = 0 → Special cases    "a" assignment:    0 →             region beyond all MaxETL influence.    2 →             origin of the Cartesian axis system.    4 →             reference to the physical target.    6 →             center-of-gravity of a physical target.    e = 1 → Acquring entity attributes    "a" assignment:    0 → C  → the acquiring entity.    2 → L.sub.C.maxetl.sbsb.C,20                  → distance from C to center of MaxETL of                    apex 20.    3 → L.sub.C.maxetl.sbsb.C,30                  → distance from C to center of MaxETL of                    apex 30.    4 → L.sub.C.maxetl.sbsb.C,40                  → distance from C to center of MaxETL of                    apex 40.    5 → L.sub.C.maxetl.sbsb.C,50                  → distance from C to center of MaxETL of                    apex 50.    6 → L.sub.C.maxetl.sbsb.C,60                  → distance from C to                    (X.sub.maxetl.sbsb.Em, Y.sub.maxetl.sbsb.Em).    9 → D.sub.t                  → distance from acquiring entity to center                    of T.    e = 2, 3, 4, 5, →              Physical target apexes referenced counterclockwise              with 2 denoting the left-most apex or the lower-left              apex if two equal left-most apexes exist.    "a" assignment:    0 → A  → reference to apex A.    1 → -- → reference to line bisector of apex A.    2 → MaxETL.sub.Az                  → loci forming MaxETL containing apex A                    and center of closest extreme inscribed                    circle.    3 → -- → extent of angle subtended by apex A.    4 → -- → area contained within MaxETL.sub.Az.    6 → etl.sub.Az                  → center of MaxETL.sub.Az.    8 → R.sub.MaxETL.sbsb.Az                  → radius of MaxETL.sub.Az.    e = 6 → External apex of the primary generating triangle.    "a" assignment:    0 → E  → reference to external apex.    1 → -- → reference to line bisector of apex E.    2 → MaxETL.sub.Em                  → loci forming MaxETL containing apex E                    and point m    3 → -- → extent of angle subtended by apex E.    4 → -- → area contained within MaxETL.sub.Em.    5 → -- → one-half of angle subtended by apex E.    6 → maxetl.sub.Em                  → reference to center of MaxETL.sub.Em.    8 → R.sub.MaxETL.sbsb.E                  → radius of MaxETL.sub.Em.    e = 7, 8 →             Largest and smallest inscribed extreme circles             of the primary generating triangle.    "a" assignment:    2 → M, N                → reference to largest inscribed                  circles identified by bisectors of                  base and nonbase-apexes respectively.    6 → m, n                → centers of circles M and N respectively.    8 → R.sub.M, R.sub.N                → radii of circles M and N respectively.    e = 9 → Implicit target.    "a" assignment:    2 → T               → reference to implicit target.    2 → t               → reference to center of implicit target.    8 → R.sub.T               → radius of implicit target.    e = 10 →           the ETL containing the external apex and the center           of the largest inscribed circle identified by bisectors           of nonbase-apexes, and    e = 11 →           an ETL of arbitrary radius containing either an apex of the           physical target or the external apex.    "a" assignment:    2 → ETA.sub.En, ETA.sub.Az                   → respecitvely (1) the ETL containing                     apex E and point n and (2) the ETL                     containing a referenced apex A and an                     arbitrary point z.    6 → etl.sub.En, etl.sub.Az                   → reference to center of ETL.sub.En and                     ETL.sub.Az respectively.    8 → R.sub.ETL.sbsb.En, R.sub.ETL.sbsb.Az                   → radious of ETL.sub.En and ETL.sub.Az                     respectively.    e = 12, 13 →             reference to largest inscribed circles identified by             biscectors of base and nonbase-apexes respectivley of             secondary generating triangle.    "a" assignment:    2 → M, N                → reference to largest and smallest circles                  respectively.    6 → m, n                → reference to center of circles M and N                  respectively.    8 → R.sub.M, R.sub.N                → radius of circles M and N respectively.    ______________________________________

Typology of Targets Covered by the Detailed Description

While the invention concerns identification of the set of uniquephysical points located within an physical target that minimizes thephysical effort expended to acquire said physcial target, the preferredprocedure by which these points are identified depends on the type ofphysical target. The following typology details physical target typesfor which preferred procedures of implementation are detailed:

1. To determine the physical effort to acquire a physical target ofcircular shape centered at location V with radius U apply prior art toobtain values of ##EQU54## and W=2×U as indicated by block 11100 of FIG.11A. 2. To determine the physical effort expended to acquire a physicaltarget of arbitrary triangular shape and arbitrary orientation apply theDetailed Analysis of the Triangle starting at block 11102 of FIG. 11A.

3. To determine the physical effort expended to acquire a physicaltarget of a convex quadrilateral shape having no pair of parallel sidesapply the Detailed Analysis of the Quadrilateral starting at block 11104of FIG. 11A.

4. To determine the physical effort expended to acquire a physicaltarget of quadrilateral shape having one pair of parallel sides at anarbitrary angle to the axis apply the Detailed Analysis of the Trapezoidstarting at block 11106 of FIG. 11A.

5. To determine the physical effort expended to acquire a physicaltarget of quadrilateral shape having two orthogonal pair of parallelsides parallel to the axis apply the Detailed Analysis of the StandardRectangle starting at block 11108 of FIG. 11.

6. To determine the physical effort expended to acquire a physicaltarget of quadrilateral shape having two pair of parallel sides atarbitrary angles to the axis apply the Detailed Analysis of theParallelogram starting at block 11110 of FIG. 11A.

Detailed Analysis of the Triangle: Procedure Commences at Block 11200:

1. Determine Parameters of Largest Inscribed Extreme Circle:

(a) Determine (X_(m),Y_(m)) by procedure 11202.

Apply Eq 13, Eq 14, and Eq 15 to determine (X_(m),Y_(m)). This islocation 12A76 and is determined by the intersection of bisectors of anytwo physical target apexes; i.e., any two of 12A21, 12A31, and 12A41.

(b) Determine R_(M) by procedure 11204.

Repetitively apply Eq 2 to obtain the length of each side of thephysical target. Apply Eq 3 to determine the angle of an arbitrary apex,A, then determine half the value of said arbitrary apex angle. Apply Eq2 to determine L_(A),m, the distance between (X_(A),Y_(A)) and(X_(m),Y_(m)). Apply Eq 4 to said half angle and L_(A),m to determineR_(M). This is conveyed by FIG. 12A where length of sides of 12A04 are##EQU55## If 12A20 is the selected apex, the apex angle is 12A23 with##EQU56## being the distance between apex 12A20 and the intersection ofangle bisectors at 12A76. ##EQU57## is the radius of 12A72, the largestcircle which can be inscribed in physical target 12A04.

2. Analyze the MaxETL of each apex in turn by iteration 11206:

From geometry recall that the midpoint (X_(d),Y_(d)) of the lineconnecting any two points, "a" and "b", located at (X_(a),Y_(a)) and(X_(b),Y_(b)) respectively is: ##EQU58##

(a) Determine (X_(maxetl).sbsb.Am, Y_(maxetl).sbsb.Am) of the currentMaxETL by procedure 11208.

Eq 8 shows the center of each MaxETL_(A), (X_(maxetl).sbsb.Am,Y_(maxetl).sbsb.Am), to be the mid-point of the line between apex A andthe center of the nearest inscribed extreme circle. Apply Eq 18 to thecurrent MaxETL to determine this location. This is illustrated in FIG.12 Part B by locations 12B26, 12B36, and 12B46 which are the mid-pointsof lines between the center, 12B96, of the largest inscribed circle,12A74, and the physical target apexes 12B20,12B30, and 12B40respectively.

(b) Determine R_(MaxETL).sbsb.Am of the current MaxETL by procedure11210.

Apply Eq 2 to (X_(m),Y_(m)) and the current (X_(maxetl).sbsb.Am,Y_(maxetl).sbsb.Am) to determine R_(MaxETL).sbsb.Am. This is illustratedin FIG. 12 Part B where MaxETL 12B22, 12B32, and 12B42 have radii##EQU59## respectively.

(c) Determine the current ##EQU60## by procedure 11212.

Repetitively apply Eq 2 to (X_(c),Y_(c)) and the current(X_(maxetl).sbsb.Am, Y_(maxetl).sbsb.Am) to determine ##EQU61## This isillustrated by FIG. 12 Part B where ##EQU62## respectively denote thedistances between the acquiring entity at 12B10 and MaxETL centers at12B26, 12B36, 12B46.

3. Identify Type of Analysis Required:

(a) For the case of no A such that ##EQU63## use procedure 11218.

The acquiring entity is outside all MaxETL_(Am) regions; i.e., region12B00 of FIG. 12 Part B. To analyze apply Section 4 "ETL Analysis of theLargest Inscribed Extreme Circle" of the Detailed Analysis of theTriangle.

(b) For the case of one A having ##EQU64##

The acquiring entity falls within one MaxETL region; i.e., in FIG. 12Part C within the area delimited by 12C22. To analyze apply Section 5"ETL Analysis of the Apex" of the Detailed Analysis of the Triangle.

4. ETL Analysis of the Largest Inscribed Extreme Circle:

The implicit target is the largest inscribed extreme circle of thephysical target. Apply Eq 2 to (X_(c),Y_(c)) and (X_(m),Y_(m)) todetermine D_(t). R_(M) is known from above. W_(t) is twice R_(M). FIG.12 Part B illustrates that for a acquiring entity located at 12B10 theimplicit target is 12B94 and results a in D_(t) of ##EQU65## and a##EQU66## 5. ETL Analysis of the Apex:

(a) Transform the axis by procedures 11222 and 11224.

Translate the axis origin to coincide with the apex, A, of the ETLcontaining the acquiring entity. Perform rotation to make the positivedirection of the transformed x-axis coincident with the bisector of apexA. For implicit target analysis of the apex it suffices to express theacquiring entity, the specified apex, and the center of the closestinscribed extreme circle in coordinates of the transformed axis.Employing lower-case letters to represent transformed coordinates, thoseskilled in the art can apply the following matrix formulation to affectthese transformations: ##EQU67## where: x_(A),y_(A) (X_(A), Y_(A))expressed in terms of the translated axis.

x_(c),y_(c) (X_(c), Y_(c)) expressed in terms of the translated axis.

x_(m),y_(m) (X_(m), Y_(m)) expressed in terms of the translated axis.

δ tan⁻¹ (Slope of Apex Bisector).

Eq 19 performs clockwise rotation. Those applying the invention mustassure direction and amount of rotation conforms to the behavior of Eq19.

FIG. 12 Part C illustrates this environment with an initial acquiringentity located at 12C10 within the area delimited by 12C22. To analyze,the X-axis is translated by 12C20_(X), and the Y-axis translated by12C20_(Y) followed by rotation of the translated axis by β degrees. Thisprocedure converts said relevant locations into the transformedlocations of FIG. 12 Part D; namely, acquiring entity location 12C10transforms to 12D10, the center of the largest inscribed circle 12C76transforms to 12D76, and apex A at 12C20 transforms to 12D20.

(b) Determine D_(t) by procedure 11226!

Expressed in terms of the transformed axis, the optimum physical targetacquisition point, t, is the intersection of the transformed x-axis andthe ETL containing transformed coordinates of A and C. Apply Eq 6 tox_(c) and y_(c) to determine (x_(t),y_(t)). Apply Eq 2 to (x_(c),y_(c))and (x_(t),y_(t)) to determine D_(t). 12D112 is the ETL containing bothapex 12D20 and acquiring entity 12D10. The optimal acquisition point is12D96, the center of the implicit target 12D94, for a D_(t) of ##EQU68##

(c) Determine W_(t) by procedure 11226.

Apply Eq 2 to (x_(A),y_(A)) and (x_(t),y_(t)) to determine ##EQU69## Ifnot previously determined, apply Eq 3 to determine the extent of theangle of apex A. Determine one-half the extent of said angle. Apply Eq 4to said half apex angle and ##EQU70## to determine the radius of theimplicit target. Set W_(t) equal to twice this radius. In FIG. 12 Part Athe extent of the angle of apex 12A20 is denoted by 12A23 with 12D25denoting half this angle. When resolved for a acquiring entity withinthe range of an MaxETL, as with FIG. 12 Part C, ##EQU71## DetailedAnalysis of the Quadrilateral: Procedure Commences at Block 11300

1. Analyze each generating triangle in turn by iteration 11302:

(a) Determine (X_(E),Y_(E)) of current generating triangle by procedure11304. Select a pair of opposite sides of the quadrilateral physicaltarget and apply Eq 11 and Eq 12 to determine (X_(E),Y_(E)). In FIG. 13Part A these are locations 13A60 and 13A120.

(b) Determine (X_(m),Y_(m)) of the base-apexes by procedure 11306.

Apply Eq 13, Eq 14, and Eq 15 to the base-apexes of the currentgenerating triangle to determine the center of the circle identified bybisectors of said apexes. In FIG. 13 centers of the two inscribedextreme circles of the baseapexes are location 13A76 as determined bybisectors 13A31 and 13A41 of apexes 13A30 and 13A40 and location 13A136as determined by bisectors 13A21 and 13A31 of apexes 13A20 and 13A30respectively.

(c) Determine (X_(n),Y_(n)) of the nonbase-apexes by procedure 11308.

Apply Eq 13, Eq 14, and Eq 15 to the nonbase-apexes of the currentgenerating triangle to determine the center of the circle identified bybisectors of said apexes. In FIG. 13A centers of the two inscribedextreme circles of the nonbase-apexes are location 13A86 as determinedby bisectors 13A21 and 13A51 of apexes 13A20 and 13A50 and location13A146 as determined by bisectors 13A41 and 13A51 of apexes 13A40 and13A60 respectively.

(d) Determine extent of the current external apex by procedure 11310.

Repetitively apply Eq 2 to obtain the length of each side of the currentgenerating triangle. Apply Eq 3 to determine the angle subtended by theexternal apex. In FIG. 13A these are ##EQU72## giving 13A63 as theextent of external apex 13A60 for one generating triangle. The othergenerating triangle has side lengths of ##EQU73## giving 13A123 as theextent of external apex 13A120 for the other generating triangle.

(e) Determine radius of inscribed extreme circle of base-apexes via11312.

Apply Eq 2 to determine ##EQU74## the distance between the current(X_(E), Y_(E)) and the center of the current largest inscribed extremecircle, (X_(m), Y_(m)), determined by base apexes. Apply Eq 4 toone-half the external angle and ##EQU75## to determine R_(M). In FIG.13A the external apex, 13A60, subtends an angle depicted by 13A63.Bisectors 13A31 and 13A41 identify the said inscribed extreme circlewith center at 13A76 and radius of ##EQU76## The external apex, 13A120,of the other generating triangle subtends an angle depicted by 13A123.Bisectors 13A31 and 13A41 determine the extreme inscribed circle to havecenter at 13A146 and radius of ##EQU77##

(f) Determine radius of inscribed extreme circle of nonbase apexes via11314.

Apply Eq 2 to determine ##EQU78## the distance between the current(X_(E), Y_(E)) and the center of the current inscribed extreme circle(X_(n), Y_(n)) identified by nonbase apexes. Apply Eq 4 to one-half theexternal angle and ##EQU79## to determine R_(N). In FIG. 13A theexternal apex, 13A60, subtends an angle depicted by 13A63. Bisectors13A21 and 13A51 identify the said inscribed extreme circle to havecenter at 13A86 and radius of ##EQU80## The external apex, 13A120, ofthe other generating triangle subtends an angle depicted by 13A123.Bisectors 13A21 and 13A31 determine the inscribed circle to have centerat 13A136 and radius of ##EQU81## 2. Identify the Primary Triangle byprocedure 11316:

Compare radii determined in steps 1(e) and 1(f) preceding to identifythe inscribed circle of each generating triangle having greatest radius.Next compare the two selected radii and take as the primary trianglethat generating triangle containing the largest inscribed circle ofsmallest radius. In FIG. 13 Part A, radius 13A78 of inscribed circle13A72 and radius 13A148 of inscribed circle 13A142 identify the largestinscribed circles. For FIG. 13 Part A the primary triangle is thegenerating triangle defined by apexes 13A60, 13A30, and 13A40. Allremaining analysis pertaining to identification of the implicit targetof a quadrilateral physical target refers exclusively to the primarytriangle.

3. Analyze the MaxETL of each base-apex in turn by iteration 11320:

(a) Determine (X_(maxetl).sbsb.Am, Y_(maxetl).sbsb.Am) for currentbase-apex by procedure 11322.

Apply Eq 18 to (X_(m),Y_(m)) and the current base-apex (X_(A),Y_(A)) todetermine (X_(maxetl).sbsb.Am, Y_(maxetl).sbsb.Am). In FIG. 13 Part Bthe base-apexes are depicted by 13B30 and 13B40 with the centers ofrelated MaxETL_(Am) at 13B36 and 13B46 respectively.

(b) Determine R_(MaxETL).sbsb.Am for the current base-apex by procedure11324.

Apply Eq 2 to (X_(A),Y_(A)) and (X_(maxetl).sbsb.Am, Y_(maxetl).sbsb.Am)of the current base-apex to determine R_(MaxETL).sbsb.Am. In FIG. 13Part B R_(MaxETL).sbsb.Am values for the MaxETL of apexes 13B30 and13B40 are ##EQU82## respectively.

(c). Determine ##EQU83## for the current base-apex by procedure 11326.

Apply Eq 2 to (X_(c),Y_(c)) and (X_(maxetl).sbsb.Am, Y_(maxetl).sbsb.Am)of the current base-apex to determine ##EQU84## of the currentbase-apex. In FIG. 13 Part B ##EQU85## represent the distances betweenthe acquiring entity, 13B10, and centers, 13B36 and 13B46, of MaxETL13B32 and 13B42 respectively.

(d) For case of one base-apex of ##EQU86## continue with block 11328.

If there exists one base-apex A such that ##EQU87## continue theimplicit target analysis of the quadrilateral from Section 5: "ETLAnalysis of the Apex" of the Detailed Analysis of the Triangle.

4. Analyze MaxETL_(E) :

(a) Determine (X_(maxetl).sbsb.Em, Y_(maxetl).sbsb.Em) by procedure11432.

Apply Eq 18 to (X_(m),Y_(m)) and (X_(E),Y_(E)) to determine(X_(maxetl).sbsb.Em, Y_(maxetl).sbsb.Em). In FIG. 13 Part B the externalapex of the primary triangle is 13B60. The MaxETL of 13B60 is 13B62 withcenter at 13B66.

(b) Determine R_(MaxETL).sbsb.Em by procedure 11434.

Apply Eq 2 to (X_(E),Y_(E)) and (X_(maxetl).sbsb.Em, Y_(maxetl).sbsb.Em)to determine R_(MaxETL).sbsb.Em. In FIG. 13 Part B the value of##EQU88##

(c) Determine ##EQU89## by procedure 11436.

Apply Eq 2 to (X_(c),Y_(c)) and (X_(maxetl).sbsb.Em, Y_(maxetl).sbsb.Em)to determine ##EQU90## In FIG. 13 Part B this distance ##EQU91##

(d) For acquiring entity located such that ##EQU92## use procedure11438.

If ##EQU93## the acquiring entity is not located within the MaxETLregion of either base-apex or the external apex. Apply Eq 2 to(X_(c),Y_(c)) and (X_(m),Y_(m)) to determine D_(t). R_(M) is known fromabove. W_(t) is twice R_(M). In FIG. 13 Part B for a acquiring entitylocated at 13B10, ##EQU94## 5. Analyze the MaxETL of each nonbase-apexin turn by iteration 11440:

Note that the physical target of FIG. 13 Part C has been scaled tobetter illustrate the portion relevant to analysis of nonbase-apexes.

(a) Determine (X_(maxetl).sbsb.An, Y_(maxetl).sbsb.An) for currentnonbase-apex by procedure 11442.

Apply Eq 18 to (X_(n),Y_(n)) and the current nonbase-apex (X_(A),Y_(A))to determine (X_(maxetl).sbsb.An, Y_(maxetl).sbsb.An). In FIG. 13 Part Cthe nonbase-apexes are at 13C20 and 13C50 with the centers of relatedMaxETL_(A) at 13C26 and 13C56 respectively.

(b) Determine R_(MaxETL).sbsb.A for the current nonbase-apex byprocedure 11444.

Apply Eq 2 to the current nonbase-apex (X_(A),Y_(A)) and its related(X_(maxetl).sbsb.An, Y_(maxetl).sbsb.An) to determineR_(MaxETL).sbsb.An. In FIG. 13 Part C, the R_(MaxETL).sbsb.An values forMaxETL of apexes 13C20 and 13C50 are ##EQU95## respectively.

(c) Determine ##EQU96## for the current nonbase-apex by procedure 11446.

Apply Eq 2 to (X_(c),Y_(c)) and the current nonbase-apex(X_(maxetl).sbsb.An, Y_(maxetl).sbsb.An) to determine ##EQU97## In FIG.13 Part C, ##EQU98## represent these distances between the acquiringentity, 13C10 and centers, 13C26 and 13C56 of MaxETLs 13C22 and 13C52respectively.

(d) For the case of one apex such that ##EQU99## select block 11448.

If there exists one nonbase-apex such that ##EQU100## continue theimplicit target analysis from Section 5: "ETL Analysis of the Apex" ofthe Detailed Analysis of the Triangle.

6. ETL Analysis of the External Apex:

(a) Determine (X_(etl).sbsb.En, Y_(etl).sbsb.En) by procedure 11450.

Apply Eq 18 to (X_(E),Y_(E)) and (X_(n),Y_(n)) to determine(X_(etl).sbsb.En, Y_(etl).sbsb.En). In FIG. 13 Part D the external apexof the primary triangle is 13D60. ETL_(En), which contains locations13D60 and 13D86, is 13D102 with center at 13D106.

(b) Determine R_(ETL).sbsb.En by procedure 11452.

Apply Eq 2 to (X_(E),Y_(E)) and (X_(etl).sbsb.En, Y_(etl).sbsb.En) todetermine R_(ETL).sbsb.En. In FIG. 13 Part D the value of ##EQU101##

(c) Determine ##EQU102## by procedure 11454.

Apply Eq 2 to (X_(C),Y_(C)) and (X_(etl).sbsb.En, Y_(etl).sbsb.En) todetermine ##EQU103## In FIG. 13 Part D the value of ##EQU104##

(d) For the case of ##EQU105## select block 11456.

The center of the implicit target, (X_(t),Y_(t)), falls on the lineconnecting the centers of the two inscribed extreme circles,(X_(n),Y_(n)) and (X_(m),Y_(m)). To analyze perform Step 5: "ETLAnalysis of the Apex" of the Detailed Analysis of the Triangle. In FIG.13 Part D the resulting implicit target is depicted by 13D94. The valueof ##EQU106##

(e) For the case of ##EQU107## use procedure 11458.

The optimum acquisition point falls within an area of the primarytriangle which is either not part of the physical target or is asub-optimum location within the physical target. For this case theoptimum physical target acquisition point is (X_(n),Y_(n)). In FIG. 13Part E for a acquiring entity located at ##EQU108## and is observed tobe less than ##EQU109## the radius of ETL_(En) 13E102. If the physicaltarget were not a truncated triangle, implicit target analysis wouldindicate an optimum hit location on line segment 13E60, 13E86, but thissegment is either not within the physical target or implies sub-optimumhit locations. Consequently, 13E86, the center of the smallest inscribedextreme circle, 13E84, is selected as implicit target. Apply Eq 2 to(X_(C),Y_(C)) and (X_(n),Y_(n)) to determine D_(t). W_(t) equals2×R_(N). In FIG. 13 Part E the value of ##EQU110## Detailed Analysis ofthe Trapezoid: Procedure Commences at Block 11500.

1. Determine the generating triangle with finite external apex byprocedure 11502:

Apply Eq 9 to any two non-adjacent sides of the physical target. Ifunequal slopes are observed the generating triangle containing thesesides has a finite external apex and select this generating triangle.Otherwise select the other generating triangle as the generatingtriangle having finite external apex. In FIG. 14 Part A the infiniteexternal apex has location at the left end of 14A60 with the othergenerating triangle having a finite external apex at 14A120.

2. Determine parameters for the generating triangle with finite externalapex:

(a) Determine (X_(E),Y_(E)) of the said generating triangle by procedure11504. Apply Eq 11 and Eq 12 to the pair of non-parallel sides of thetrapezoidal target to determine (X_(E),Y_(E)) of the finite externalapex. In FIG. 14 Part A the finite external apex is at location 14A120.

(b) Determine (X_(m),Y_(m)), (X_(n),Y_(n)) of said generating triangleby procedure 11506. Apply Eq 13, Eq 14, and Eq 15 to the base-apexes ofsaid generating triangle to determine the center of the circleidentified by bisectors of the base-apexes. Apply Eq 13, Eq 14, and Eq15 to the nonbase-apexes of said generating triangle to determine thecenter of the circle identified by bisectors of nonbase-apexes. In FIG.14 Part A the bisectors of base-apexes 14A20 and 14A30 are lines 14A21and 14A31 respectively and determine the center of inscribed extremecircle 14A132 to be location 14A136. The bisectors of nonbase-apexes14A50 and 14A40 are lines 14A51 and 14A41 respectively and determine thecenter of inscribed extreme circle 14A142 to be location 14A146.

(c) Determine R_(M) and R_(N) of said generating triangle by procedure11508. Repetitively apply Eq 2 to determine the length of each side ofsaid generating triangle. Apply Eq 3 to determine the angle subtended bythe external apex of said generating triangle. Repetitively apply Eq 2to determine the distance between the external apex and the centers ofthe two inscribed extreme circles identified by apex bisectors. Selectone of the inscribed extreme circles and determine its radius byapplication of Eq 4 to one-half the external apex angle and the distancebetween the external apex and the center of said circle. Repeat thisprocess to determine the radius of the other inscribed extreme circle.In FIG. 14 Part A the said generating triangle is identified by apexes14A120, 14A20, and 14A30. The circle identified by base apexes, 14A142,has radius ##EQU111## while the circle identified by nonbase apexes,14A132, has radius ##EQU112##

3. Determine parameters for the generating triangle with infiniteexternal apex:

(a) Determine (X_(m),Y_(m)), (X_(n),Y_(n)) of said generating triangleby procedure 11510.

Apply Eq 13, Eq 14, and Eq 15 to the base-apexes of said generatingtriangle to determine the center of the circle identified by bisectorsof these apexes. Apply Eq 13, Eq 14, and Eq 15 to the nonbase-apexes ofsaid generating triangle to determine the center of the circleidentified by bisectors of these apexes. In FIG. 14 Part A the bisectorsof base-apexes 14A30 and 14A40 are lines 14A31 and 14A41 respectivelyand determine the center of inscribed extreme circle 14A72 to belocation 14A76. The bisectors of nonbase-apexes 14A20 and 14A50 arelines 14A21 and 14A51 respectively and determine the center of inscribedextreme circle 14A82 to be location 14A86.

(b) Determine R_(M) and R_(N) of said generating triangle by procedure11512.

Apply Eq 2 to determine the length of the side between the base-apexesof the generating triangle with infinite external apex. Repetitivelyapply Eq 2 to obtain the distance between each base-apex and the centerof the inscribed extreme circle identified by bisectors of these apexes.Apply Eq 3 and determine one-half the angle of a base-apex. Apply Eq 4to determine the radius of the inscribed circle. In FIG. 14 Part A thelengths of the lines determined are, ##EQU113## Designator 14A33 depictsone-half the angle of apex 14A30. The radius of all circles which can beinscribed between the parallel sides of the physical target are denotedby ##EQU114##

4. Identify the primary triangle by procedure 11514:

Identify the extreme circle in each generating triangle of greatestradius. Select as the primary triangle that generating trianglecontaining the largest inscribed circle of smallest radius. Allremaining analysis pertaining to identification of the implicit targetof the trapezoidal target refers only to the primary triangle. In FIG.14, the generating triangle with infinite external apex has ##EQU115##as radius of its largest inscribed extreme. The generating triangle withfinite external apex has ##EQU116## as radius of 14A142, its largestinscribed extreme circle. In FIG. 14 the generating triangle withinfinite external apex is the primary triangle.

5. Identify Type of Analysis Required Based on Primary TriangleIdentification:

(a) For case of the primary triangle having finite external apex selectblock 11516.

Continue analysis at: Section 3: "Analyze MaxETL of Each Base-Apex inTurn" of the Detailed Analysis of the Quadrilateral.

(b) For case of a primary triangle having infinite external apex.

Continue analysis at: Section 6: "Transform Axis" of the DetailedAnalysis of the Trapezoid following.

6. Transform axis by procedures 11518 and 11520:

Apply Eq 18 to find the midpoint of the line connecting (X_(m),Y_(m))and (X_(n),Y_(n)), define this location as point "K". Apply Eq 19 totranslate the axis to location K and rotate the axis by the slope of theparallel sides of the primary triangle. In FIG. 14 Part A locations14A86 and 14A76 depict n and m respectively with location 14A06depicting K. Rotation is by the amount depicted by 14A63. FIG. 14 Part Bdepicts the physical target configuration after axis transformation.

7. Analyze the MaxETL of each apex in turn by iteration 11522:

(a) Determine (x_(maxetl).sbsb.Az, y_(maxetl).sbsb.Az) of current apexMaxETL by procedure 11524.

Apply Eq 18 to each (x_(A),y_(A)) and the center of the nearestinscribed extreme circle to determine each (x_(maxetl).sbsb.Az,y_(maxetl).sbsb.Az) where z is the closest of m or n to the current A.In FIG. 14 Part A these are locations 14B26, 14B36, 14B46, and 14B56.

(b) Determine R_(MaxETL).sbsb.Az of the current MaxETL by procedure11526.

Apply Eq 2 to the current apex location (x_(A),y_(A)) and its related(x_(maxetl).sbsb.Az, y_(maxetl).sbsb.Az). In FIG. 14 Part B values ofR_(MaxETL).sbsb.Az are ##EQU117##

(c) Determine ##EQU118## of the current MaxETL by procedure 11528.

Apply Eq 2 to (x_(C),y_(C)) and the current (x_(maxetl).sbsb.Az,y_(maxetl).sbsb.Az) to determine the length of each ##EQU119## In FIG.14 Part D values of ##EQU120## for the MaxETL of apexes 14D20, 14D30,14D40, 14D60 respectively.

8. Determine if (X_(c), Y_(c)) is within a MaxETL:

(a) For the case of one A such that ##EQU121## select block 11530.

The acquiring entity falls within the MaxETL region of one of thephysical target apexes Continue implicit target analysis at: Section 5:"ETL Analysis the Apex" of the Detailed Analysis of the Triangle. InFIG. 14 Part C the acquiring entity lies within the MaxETL of apex14C30; i.e., within the region delimited by 14C32. For this acquiringentity location the implicit target is 14C94 with D_(t) equal ##EQU122##and ##EQU123##

(b) For the case of no A such that ##EQU124##

The acquiring entity falls outside all MaxETL_(A) regions; asexemplified in FIG. 14 Part D by the 14D00 region. To analyze apply:Section 9: "ETL Analysis of the Inscribed Extreme Circle" of theDetailed Analysis of the Trapezoid following.

9. ETL Analysis of the Inscribed Extreme Circle:

(a) For the case of (x_(C) <x_(n)) use procedure 11532.

For this case the acquiring entity is located to the left of x_(n).Implicit target analysis determines the optimal traverse is to n, thecenter of the left-most inscribed circle. Apply Eq 2 to (x_(C),y_(C))and (x_(n),y_(n)) to determine D_(t). W_(t) is twice the radius of saidcircle. In FIG. 14 Part D the optimum traverse is from the acquiringentity, 14D10, to the center, 14D96, of implicit target, 14D94.##EQU125## W_(t) is twice the radius of the implicit target; i.e.,##EQU126##

(b) For the case of (x_(c) >x_(m)) use procedure 11534.

For this case the acquiring entity is located to the right of x_(m).Implicit target analysis determines that the optimal traverse is to thecenter, m, of the right-most inscribed circle. Apply Eq 2 to(x_(C),y_(C)) and (x_(m),y_(m)) to determine D_(t). W_(t) is twice theradius of said circle. This scenario is not depicted by FIG. 14 butbeing the mirror image of the case of (x_(c) <x_(n)), D_(t) equals thedistance between the acquiring entity and the right-most inscribedextreme circle 14B72 with center at 14B76. As with the (x_(c) <x_(n))scenario, ##EQU127##

(c) For the case of (x_(n) <x_(C) <x_(m)) use procedure 11536.

For this case the acquiring entity is located on or to the right ofx_(n) and on or to the left of x_(m). Implicit target analysisdetermines that the optimum traverse is along the normal to the lineconnecting the centers of points m and n. D_(t) is the length of thenormal between y_(c) and the x-axis; namely the value of y_(c). W istwice the radius of any circle inscribed between the trapezoid physicaltarget's parallel sides. This scenario is depicted by FIG. 14 Part Ewhere the optimum traverse gives ##EQU128## namely the traverse from theacquiring entity, 14E10, to the center, 14E96, of the implicit target14E94. W_(t) is twice the radius of the implicit target; i.e.,##EQU129## Detailed Analysis of the Standard Rectangle: ProcedureCommences at Block 11600.

For vertically elongated physical targets; i.e., AR<1, designate thetop-most inscribed extreme circle as M and its center by location m.Similarly, designate the bottom-most inscribed extreme circle as N andits center by location n. For horizontally elongated physical targets;i.e., AR>1, designate the left-most inscribed extreme circle as M andits center by location m. Similarly, designate the right-most inscribedextreme circle as N and its center by location n.

1. Translate axis by procedure 11602:

Apply Eq 18 to determine the mid-point of the physical target'shorizontal and vertical dimensions. Without rotation apply Eq 19 totranslate the axis origin to said mid-point. In FIG. 15 Part A saidmid-point is depicted by 15A06.

2. Reflect acquiring entity location by procedure 11604.

Perform the following assignments: u_(C) =|x_(C) |, v_(C) =|y_(C) | toposition the acquiring entity in quadrant 1 of the translated axis. Oneach of the separate sheets of FIG. 15 the diagram of the upper portion;i.e., Parts A, C, E, and G, depict an initial acquiring entity positionbefore reflection while the lower portion; i.e., Parts B, D, F, and H,depict the acquiring entity location after reflection. All subsequentanalysis is performed only on the upper right physical target apex.Define this apex as "K".

3. Identify the primary triangle by procedure 11606.

Apply Eq 2 to any two adjacent sides of the physical target. The primarytriangle is the generating triangle which contains the longest sides ofthe physical target. In FIG. 15 Part A sides 15A30, 15A20 and 15A40,15A50 represent segments of the parallel sides of the primary triangle.The left end of line 15A61 is defined as the infinitely remote externalapex of the primary generating triangle.

4. Determine parameters of the inscribed extreme circles of the primarytriangle:

(a) Determine R_(M) and R_(N) using procedure 11608.

All inscribed circles have a radius equal to one-half the radius of thephysical target's narrow dimension. For the translated axis, when x_(K)>y_(K) the resulting radius is R_(M) =y_(K) and when x_(K) <y_(K) theresulting radius is R_(M) =x_(K). To illustrate from FIG. 15 Part B,since the physical target is elongated horizontally the radius ofcircles inscribed within the primary triangle is 15A40_(y) ; i.e., widthis ##EQU130## the physical target height.

(b) Determine (x_(m),y_(m)) by procedure 11610.

For vertically elongated physical targets: (x_(m),y_(m))=(0,(y_(K)-x_(K))).

For horizontally elongated physical targets: (x_(m),y_(m))=((x_(K)-y_(K)),0).

5. Analyze MaxETL_(Km) :

(a) Determine (x_(max) etl.sbsb.Km, y_(max) etl.sbsb.Km) by procedure11612.

Apply Eq 18 to (x_(K),y_(K)) and (x_(m),y_(m)) to determine(x_(maxetlL).sbsb.Km, y_(maxetl).sbsb.Km). Because this location iscommon to any scenario of initial acquiring entity location it isdepicted as location 15D46, 15F46, and 15H46 in FIG. 15 Parts D, F, andH respectively.

(b) Determine R_(MaxETL).sbsb.Km by procedure 11614.

Apply Eq 2 to (x_(K),y_(K)) and (x_(maxetlL).sbsb.Km,y_(maxetl).sbsb.Km) to determine R_(MaxETL).sbsb.Km. Because this valueis common to any scenario of initial acquiring entity location it isdepicted as location 15D48, 15F48, and 15H48 in FIG. 15 Parts D, F, andH respectively.

(c) Determine ##EQU131## by procedure 11616.

Apply Eq 2 to (x_(C), y_(C)) and (x_(maxetl).sbsb.k,y_(maxetl).sbsb.k)to determine ##EQU132## These lengths depend upon the initial acquiringentity location and are depicted as ##EQU133## in FIG. 15 Parts D, F,and H respectively.

6. Identify type of analysis required:

(a) For the case of ##EQU134## select block 11618.

The acquiring entity falls within the region delimited by MaxETL_(Km).To analyze apply: Section 5: "ETL Analysis of the Apex" of the DetailedAnalysis of the Triangle. FIG. 15 Part C illustrates this scenario. InFIG. 15 Part D the resulting implicit target is depicted by 15D94 with##EQU135## and ##EQU136##

(b) For the case of ##EQU137##

The acquiring entity falls outside the MaxETL_(K) region. To analyzeapply: Section 7: "ETL Analysis of the Inscribed Extreme Circle" of theDetailed Analysis of the Standard Rectangular Target following.

7. ETL Analysis of the Inscribed Extreme Circle:

(a) Horizontally elongated physical target:

For the case of (u_(C) ≦x_(m)), use procedure 11620.

The acquiring entity is outside influence of all MaxETL regions at alocation from which a normal traverse to the line segment connecting theaxis origin and the center of the right-most inscribed circle ispossible. This case gives D_(t) =v_(C) and W_(t) =2×y_(K). FIG. 15 PartE illustrates this scenario. In FIG. 15 Part F.the resulting implicittarget is depicted by 15F94. D_(t) equals ##EQU138## and ##EQU139## For(u_(c) >x_(m)), use procedure 11622.

The acquiring entity is outside influence of all MaxETL regions at alocation from which a normal traverse to the line segment connecting theaxis origin and the center of the right-most inscribed circle is notpossible. This case give ##EQU140## and W_(t) =2×y_(K). FIG. 15 Part Gillustrates this scenario. In FIG. 15 Part H the resulting implicittarget is depicted by 15H94. ##EQU141## and ##EQU142##

(b) Vertically elongated physical target:

For the case of (v_(c) ≦y_(m)) use procedure 11624.

The acquiring entity is outside influence of all MaxETL regions at alocation from which a normal traverse to the line segment connecting theaxis origin and the center of the top-most inscribed circle is possible.This case, which is not illustrated, gives D_(t) =u_(c) and W_(t)=2×x_(K).

For (v_(C) >y_(m)), use procedure 11626.

The acquiring entity is outside influence of all MaxETL regions at alocation from which a normal traverse to the line segment connecting theaxis origin and the center of the top-most inscribed circle is notpossible. This case, which is not illustrated, gives ##EQU143## DetailedAnalysis of the Parallelogram: Procedure Commences at Block 11700.

1. Determine parameters of inscribed extreme circles of the primarytriangle:

(a) Determine lengths of physical target sides by procedure 11702.

Repetitively apply Eq 2 to obtain the length of a side in each pair ofparallel sides. In FIG. 16 Part A side lengths are ##EQU144##

(b) Determine the primary triangle by procedure 11704.

The primary triangle is the generating triangle identified by thelongest pair of parallel sides of the parallelogram. In FIG. 16 Part Athe primary generating triangle has 16A30, 16A20 and 16A40, 16A50 asline segments of its parallel sides.

(c) Determine (X_(m), Y_(m)) of base-apexes by procedure 11706.

Apply Eq 13, Eq 14, and Eq 15 to the base-apexes of the primary triangleto determine the center of the inscribed extreme circle identified bybisectors of these apexes. In FIG. 16 Part A the bisectors ofbase-apexes 16A30 and 16A40 are lines 16A31 and 16A41 respectively anddetermine the center of inscribed extreme circle 16A72 to be location16A76.

(d) Determine (X_(n), Y_(m)) of nonbase-apexes by procedure 11708.

Apply Eq 13, Eq 14, and Eq 15 to the nonbase-apexes of the primarytriangle to determine the center of the inscribed extreme circleidentified by bisectors of these apexes. In FIG. 16 Part A the bisectorsof nonbase-apexes 16A20 and 16A50 are lines 16A21 and 16A51 respectivelyand determine the center of inscribed extreme circle 16A82 to belocation 16A86.

(e) Determine radius of inscribed extreme circles using procedure 11710.

Apply Eq 2 and obtain the length of the side between the base-apexes ofthe generating triangle. Repetitively apply Eq 2 to obtain the distancebetween each base-apex and the center of the inscribed extreme circleidentified by bisectors of these apexes. Apply Eq 3 and determine theangle of a base-apex. Apply Eq 4 to one-half the base angle apex justdetermined and ##EQU145## to determine the radius of the inscribedcircle. In FIG. 16 Part A the lengths of the lines specified are##EQU146## Designator 16A33 depicts one-half the angle of apex 16A30.The radius of all circles which can be inscribed between the parallelsides of the physical target is denoted by ##EQU147##

2. Adjust Physical target Environment:

(a) Translate and rotate axis by procedure 11712.

Apply Eq 18 to find the midpoint of the line connecting (X_(m), Y_(m))and (X_(n), Y_(n)), define this location as point "K". Apply Eq 9 to endpoints of a long side of the primary triangle. Apply Eq 19 to translatethe axis to location K and rotate the axis by the slope of the parallelsides of the primary triangle. In FIG. 16 Part A locations 16A76 and16A86 depict m and n respectively with location 16A06 depicting K.Rotation is by the angle depicted by 16A23. FIG. 16 Part B depicts thephysical target configuration after this transformation with 16B02denoting the origin of the transformed axis.

(b) Reflect acquiring entity and physical target by procedure 11714.

Assign (u_(c) =x_(c)) and (v_(c) =y_(c)). If (u_(c) <0) assign (u_(c)=|u_(c)) and for each of the four physical target apex assign (x_(b)=-1×x_(a)). If (v_(c) <0) assign (v_(c) =|v_(c) |) and for each of thefour physical target apex assign (y_(b) =-1×y_(a)). In FIG. 16 Part Cthe initial acquiring entity location is in Quadrant 1 and no reflectionis performed. FIG. 16 Part G depicts the case where the acquiring entityis initially located in Quadrant 2 which entails reflection only aboutthe y-axis. FIG. 16 Part H depicts the post-reflection representation ofthis case by showing apexes 16H50 and 16H40 as being exchanged andapexes 16H20 and 16H30 being exchanged. FIG. 16 Part E depicts the casewhere the acquiring entity is located in Quadrant 3 and is reflectedabout both the x-axis and the y-axis. FIG. 16 Part F depicts thepost-reflection representation of this case by showing apexes 16F20 and16F40 as being exchanged and apexes 16F50 and 16F30 as being exchanged.All subsequent analysis relates only to the positive half plain of thetransformed and reflected axis system. Define the upper right apex as"K".

3. Analyze the MaxETL of each base-apex in turn by iteration 11716:

After appropriate axis transformation and appropriate reflection theprimary triangle has sides parallel to the translated x-axis and theacquiring entity is located in quadrant 1. Assume the infinitely distantapex of said primary triangle is at (-x.sub.∞, 0). Base-apex are thusthe two right-most physical target apexes.

(a) Determine (x_(maxetl).sbsb.Am,y_(maxetl).sbsb.Am) of currentbase-apex MaxETL by procedure 11718.

Apply Eq 18 to (x_(m),y_(m)) and the current base-apex (x_(A),y_(A)) todetermine its (x_(maxetl).sbsb.Am,y_(maxetl).sbsb.Am). In FIG. 16 PartD, Part F, and Part H (x_(maxetl).sbsb.Am,y_(maxetl).sbsb.Am) values forbase-apexes are ##EQU148## respectively. In FIG. 16 Part B base-apexesare depicted by l6B30 and 16B40 with the centers of related MaxETL_(Am)at 16B36 and 16B46 respectively.

(b) Determine R_(MaxETL).sbsb.Am of current base-apex MaxETL byprocedure 11720.

Apply Eq 2 to (x_(A),y_(A)) and the current base-apex(x_(maxetl).sbsb.Am,y_(maxetl).sbsb.Am) to determine itsR_(MaxETL).sbsb.Am. In FIG. 16 Part D, Part F, and Part HR_(MaxETL).sbsb.Am values for base-apexes are ##EQU149## respectively.(c) Determine ##EQU150## for current base-apex MaxETL using procedure11722.

Apply Eq 2 to (u_(c),v_(c)) and the current (x_(maxetl).sbsb.Am,y_(maxetl).sbsb.Am) to determine its ##EQU151## In FIG. 16 Part D, PartF, and Part H ##EQU152## values for base apexes are ##EQU153##respectively.

4. Identify type of analysis required:

(a) For the case of one apex such that ##EQU154## use 11724 Theacquiring entity falls within the region delimited by a MaxETL. Continuethe implicit target analysis of the parallelogram from Section 5: "ETLAnalysis of the Apex" of the Detailed Analysis of the Triangle. FIG. 16Part C illustrates this scenario which does not entail reflection toproduce the environment indicated by FIG. 16 Part D. The ETL Analysis ofthe Apex determines the optimum hit point to be 16D96, the center ofimplicit target 16D94. ##EQU155##

(b) For the case of ##EQU156## and (0≦u_(C) ≦x_(m)) use 11726.

The x-value of the acquiring entity location falls on or to the right ofthe y-axis and on or to the left of the x-value of the center of theright-most inscribed extreme circle. For this case: D_(t) =v_(C) andW_(t) =2×y_(K). FIG. 16 Part E depicts a acquiring entity transformed tolocation 16E10. Reflection of the acquiring entity and physical targetabout both the x-axis and the y-axis produces the environment indicatedby FIG. 16 Part F. The shortest distance to the implicit target is anormal traverse to the x-axis, thus the distance traversed is they-component of the transformed, reflected acquiring entity locationi.e., to 16F96, the center of implicit target 16F94 for a D_(t) value of∥16F19∥. With the implicit target being within the physical target sidesparallel to the x-axis, the radius of said implicit target is they-component of the location of the upper-right apex location; i.e.##EQU157##

(c) For the case of ##EQU158## and (x_(m) <u_(c)) use procedure 11728.

The x-value of the acquiring entity location falls to the right of thex-value of the center of the right-most inscribed extreme circle. Forthis case: ##EQU159## FIG. 16 Part E depicts a acquiring entityinitially located at 16G10. Reflection of the acquiring entity andphysical target about the x-axis and y-axis gives the environmentillustrated by FIG. 16 Part H. The shortest distance to the implicittarget is the length of the traverse to the center of the right-mostinscribed extreme circle; i.e., to 16H96, the center of implicit target16H94 for a D_(t) value of ##EQU160## With the implicit target beingbounded by sides parallel to the x-axis, the radius of said implicittarget is the length of any normal from the long side of the physicaltarget to the x-axis; a distance indicated by the y-component of thelocation of the upper-right apex location; i.e. ##EQU161##

The invention has been described in an exemplary and preferredembodiment, but is not limited thereto. Those skilled in the art willrecognize that a number of additional modifications and improvements canbe made in the invention without departure from the essential spirit andscope. The scope of the invention should only be limited by the appendedset of claims. ##SPC1##

I claim:
 1. A computer-implemented method for selecting from a pluralityof different computer-human interfaces an optimum computer-humaninterface that provides a low level of aggregated physical effort forthe human to acquire and manipulate a displayed physical target,comprising the steps of:identifying the operative acquiring entity;identifying the start location of said acquiring entity; iterativelyperforming the steps of each task of said pre-defined standard testsuite utilizing each of said plurality of computer-human interfaces:(a)inscribing a first circle of maximum radius within said physical targetof one of said computer-human interface; (b) determining radius ofinscribed said first circle; (c) determining distances from each saidapex of said physical target to center of inscribed said first circle;(d) generating for each said apex a maximum equi-target locus circulararc centered at the midpoint of the line connecting the respective saidapex and the center of said first circle with radius of one-half eachrespective said distances; (e) if said acquiring entity is located onborder or outside of each said maximum equi-target locus circular arc,determining the modal place of acquisition to be center of inscribedsaid first circle; (f) if respective said maximum equi-target locuscircular arc contains said acquiring entity, determining the modal placeof acquisition to be center of a second circle inscribed within saidphysical target, with the center of inscribed said second circle being afunction of the horizontal displacement and vertical displacement ofsaid acquiring entity from said apex; (g) determining said level ofphysical effort of one of said computer-human interface needed toacquire said physical target as a relation of said distance between thestart location of said acquiring entity to said selected modal place ofacquisition and the radius of said circle identified by said selectedmodal place; (h) aggregating and storing said level of physical effortso determined of one of said computer-human interface; (i) comparingsaid stored level of aggregated physical effort of another saidcomputer-human interface; (j) selecting said optimum computer-humaninterface that provides a low said level of aggregated physical effortas determined by said comparing step i.
 2. The method of claim 1 furtherincluding the steps of:identifying a plurality of computer-humanphysical operations which represent different ways for said human toacquire and manipulate said displayed physical target; selecting onefrom said plurality of computer-human physical operations for a physicaleffort evaluation; and using the selected one to specify said physicaltarget.
 3. A computer-implemented method for selecting from a pluralityof different computer-human interfaces an optimum computer-humaninterface that provides a low level of aggregated physical effort forthe human to acquire and manipulate a displayed physical target,comprising the steps of:identifying the operative acquiring entity;identifying the start location of said acquiring entity; iterativelyperforming the steps of each task of said pre-defined standard testsuite utilizing each of said plurality of computer-human interfaces:(a)inscribing a first circle of maximum radius within said physical targetof one of said computer-human interface; (b) determining radius ofinscribed said first circle; (c) for each apex having both sides of saidapex tangent with said first circle, determining distances from eachsaid apex to center of inscribed said first circle; (d) generating foreach said apex a maximum equi-target locus circular arc centered at themidpoint of the line connecting the respective said apex and the centerof said first circle with radius of one-half each respective saiddistances; (e) if said acquiring entity is located on border or outsideof each said maximum equi-target locus circular arc, determining themodal place of acquisition to be center of inscribed said first circle;(f) if respective said maximum equi-target locus circular arc containssaid acquiring entity, determining the modal place of acquisition to becenter of a second circle inscribed within said physical target, withthe center of inscribed said second circle being a function of thehorizontal displacement and vertical displacement of said acquiringentity from said apex; (g) absent identification of a valid modal placeof acquisition as determined by steps (a)-(f) and when all sides of saidphysical target are not tangent to said first circle, inscribing a thirdcircle of minimum radius having tangency with three sides of saidphysical target; (h) determining radius of said third circle; (i) foreach apex having both sides of said apex tangent with said third circle,determining distances from each said apex to center of inscribed saidthird circle; (j) generating for each said apex a maximum equi-targetlocus circular arc centered at the midpoint of the line connecting therespective said apex and the center of said third circle with radius ofone-half each respective said distances; (k) if respective said maximumequi-target locus circular arc contains said acquiring entity,determining the modal place of acquisition to be center of a forthcircle inscribed within said physical target, with the center ofinscribed said forth circle being a function of the horizontaldisplacement and vertical displacement of said acquiring entity fromsaid apex; (l) absent identification of a said modal place ofacquisition as determined by steps (g)-(k), determining remoteintersection point as defined by intersection of two non-adjacent sidesof said physical target, with each said side being tangent to both saidfirst and third circles; (m) determining distance from said remoteintersection point to center of inscribed said third circle; (n)generating for said remote intersection point a maximum equi-targetlocus circular arc centered at the midpoint of the line connecting saidremote intersection point and the center of said third circle withradius of one-half said distance; (o) if said acquiring entity islocated on border or within maximum equi-target locus circular arccontaining said remote intersection point and if intersection betweenequi-target locus circular arc containing said remote intersection pointis positioned on the line connecting said remote intersection point andcenter of said third circle, determining the modal place of saidacquisition to be center of inscribed said third circle; (p) if saidacquiring entity is located on border or within maximum equi-targetlocus circular arc containing said remote intersection point and ifintersection between equi-target locus circular arc containing saidremote intersection point is positioned on the line connecting saidcenter of said third and center of said first circle, determining themodal place of said acquisition to be center of a fifth circle inscribedwithin said physical target; (q) determining said level of physicaleffort of one of said computer-human interface needed to acquire saidphysical target as a relation of said distance between the startlocation of said acquiring entity to said selected modal place and theradius of said circle identified by said selected modal place; (r)aggregating and storing said level of physical effort so determined ofone of said computer-human interface; (s) comparing said stored level ofaggregated physical effort of another said computer-human interface; (t)selecting said optimum computer-human interface that provides a low saidlevel of aggregated physical effort as determined by said comparing steps.
 4. The method of claim 3 further including the steps of:identifying aplurality of computer-human physical operations which representdifferent ways for said human to acquire and manipulate said displayedphysical target; selecting one from said plurality of computer-humanphysical operations for a physical effort evaluation; and using theselected one to specify said physical target.
 5. A computer-implementedmethod for evaluating performance of a human using a computer-humaninterface based on the physical effort for the human to acquire andmanipulate a displayed physical target, comprising the stepsof:identifying the operative acquiring entity; identifying the startlocation of said acquiring entity; iteratively performing the steps ofeach task of said pre-defined standard test suite utilizing each of saidplurality of computer-human interfaces:(a) inscribing a first circle ofmaximum radius within said physical target of one of said computer-humaninterface; (b) determining radius of inscribed said first circle; (c)determining distances from each said apex of said physical target tocenter of inscribed said first circle; (d) generating for each said apexa maximum equi-target locus circular arc centered at the midpoint of theline connecting the respective said apex and the center of said firstcircle with radius of one-half each respective said distances; (e) ifsaid acquiring entity is located on border or outside of each saidmaximum equi-target locus circular arc, determining the modal place ofacquisition to be center of inscribed said first circle; (f) ifrespective said maximum equi-target locus circular arc contains saidacquiring entity, determining the modal place of acquisition to becenter of a second circle inscribed within said physical target, withthe center of inscribed said second circle being a function of thehorizontal displacement and vertical displacement of said acquiringentity from said apex; (g) determining said level of physical effort ofone of said computer-human interface needed to acquire said physicaltarget as a relation of said distance between the start location of saidacquiring entity to said selected modal place of acquisition and theradius of said circle identified by said selected modal place; (h)aggregating and storing said level of physical effort so determined ofone of said computer-human interface; (i) determining the actualphysical effort expended by said human to acquire said physical target;(j) comparing said computed physical effort with said actual physicaleffort to evaluate said performance of said human.
 6. Acomputer-implemented method for evaluating performance of a human usinga computer-human interface based on the physical effort for the human toacquire and manipulate a displayed physical target, comprising the stepsof:identifying the operative acquiring entity; identifying the startlocation of said acquiring entity; iteratively performing the steps ofeach task of said pre-defined standard test suite utilizing each of saidplurality of computer-human interfaces:(a) inscribing a first circle ofmaximum radius within said physical target of one of said computer-humaninterface; (b) determining radius of inscribed said first circle; (c)for each apex having both sides of said apex tangent with said firstcircle, determining distances from each said apex to center of inscribedsaid first circle; (d) generating for each said apex a maximumequi-target locus circular arc centered at the midpoint of the lineconnecting the respective said apex and the center of said first circlewith radius of one-half each respective said distances; (e) if saidacquiring entity is located on border or outside of each said maximumequi-target locus circular arc, determining the modal place ofacquisition to be center of inscribed said first circle; (f) ifrespective said maximum equi-target locus circular arc contains saidacquiring entity, determining the modal place of acquisition to becenter of a second circle inscribed within said physical target, withthe center of inscribed said second circle being a function of thehorizontal displacement and vertical displacement of said acquiringentity from said apex; (g) absent identification of a valid modal placeof acquisition as determined by steps (a)-(f) and when all sides of saidphysical target are not tangent to said first circle, inscribing a thirdcircle of minimum radius having tangency with three sides of saidphysical target; (h) determining radius of said third circle; (i) foreach apex having both sides of said apex tangent with said third circle,determining distances from each said apex to center of inscribed saidthird circle; (j) generating for each said apex a maximum equi-targetlocus circular arc centered at the midpoint of the line connecting therespective said apex and the center of said third circle with radius ofone-half each respective said distances; (k) if respective said maximumequi-target locus circular arc contains said acquiring entity,determining the modal place of acquisition to be center of a forthcircle inscribed within said physical target, with the center ofinscribed said forth circle being a function of the horizontaldisplacement and vertical displacement of said acquiring entity fromsaid apex; (l) absent identification of a said modal place ofacquisition as determined by steps (g)-(k), determining remoteintersection point as defined by intersection of two non-adjacent sidesof said physical target, with each said side being tangent to both saidfirst and third circles; (m) determining distance from said remoteintersection point to center of inscribed said third circle; (n)generating for said remote intersection point a maximum equi-targetlocus circular arc centered at the midpoint of the line connecting saidremote intersection point and the center of said third circle withradius of one-half said distance; (o) if said acquiring entity islocated on border or within maximum equi-target locus circular arccontaining said remote intersection point and if intersection betweenequi-target locus circular arc containing said remote intersection pointis positioned on the line connecting said remote intersection point andcenter of said third circle, determining the modal place of saidacquisition to be center of inscribed said third circle; (p) if saidacquiring entity is located on border or within maximum equi-targetlocus circular arc containing said remote intersection point and ifintersection between equi-target locus circular arc containing saidremote intersection point is positioned on the line connecting saidcenter of said third and center of said first circle, determining themodal place of said acquisition to be center of a fifth circle inscribedwithin said physical target; (q) determining said level of physicaleffort of one of said computer-human interface needed to acquire saidphysical target as a relation of said distance between the startlocation of said acquiring entity to said selected modal place and theradius of said circle identified by said selected modal place; (r)aggregating and storing said level of physical effort so determined ofone of said computer-human interface; (s) determining the actualphysical effort expended by said human to acquire said physical target;(t) comparing said computed physical effort with said actual physicaleffort to evaluate said performance of said human.